Yes.
At least nearly always.
This is done less often in the US than in Britain, where one will hear it done to great effect in most English cathedral and collegiate choirs.
Often the grammar does not follow the musical phrase when singing hymn tunes. When this happens the grammar takes precedence. If there is a series of commas, one may wish to pick the best one(s) to observe lest the effect is too choppy. Otherwise sing as you would read a sentence. This means singing legato and without a break even when going from one musical phrase or line of the tune to the next if there is no punctuation in the text.

In your example above, I would sing with a very slight enunciation for the first comma, but a complete break for the next two, like this:
Come, Holy Ghost,| Creator blest,| and in our hearts take up thy rest...
This causes a greater consciousness that one is, in fact, addressing the Holy Ghost, saying something nice about him, and requesting something of him. It makes of the text the purposeful supplication that it is rather than the string of words that it all too often becomes.

The idea is to sing the text just as if one were reading a poem, which, of course, is what a hymn is. In fact, it is a good exercise to have one's choir read the stanzas of the hymns they sing, observing every punctuation and eliding lines when there isn't punctuation, just as one would in reading poetry, then to sing it the same way.

With consistent and careful playing of the organ I have even accustomed entire congregations to sing in this manner. It really makes hymn singing much more meaningful and exciting.

Many hymns, 'Once in royal David's city' comes to mind, present quite a fascinating array of places to elide from one musical phrase to the next, or to break within one.
A text really comes to life when sung in this manner, and realising that what one is singing really does have a carefully written and intentionally expressed meaning can make singing of hymns much more fruitful and gladsome.

(And, if certain persons sang and played hymns with as much care and respect for their literary content as they do when singing other parts of the mass or the lectionary, they would have much more respect for their hymnody - and would be more careful in their choice of hymns.)

One might add that one can always tell if an organist is singing the text or even thinking about it as he or she drives through an entire stanza without missing a beat and! hardly allows time for breath or reflection before rushing from one stanza to the next. Such people have no business being church musicians because they aren't, actually.

Getting back to commas, I often observe them in Gregorian tunes as well as modern ones.

Comprehending and communicating the literary beauty and the sense of the text always has primacy.

Commas should be sung for sense. That said, there is a school of thought in Catholic hymn singing to sing phrases with a sense of arsis and thesis like chant (of course, this means the organ is subordinated to the needs of the vocal line - first conceiving how the hymn would best be sung a cappella). This is easier with certain tunes than others; then again, that's a reason some folks preferred certain tunes to others. Ted Marier comes to mind as a considered practitioner of this.

Then there are the aging singers who have to breathe at every fourth word. I don't have a solution for that. Although it does surprise me that otherwise healthy people are willing to let their lung capacity diminish and do nothing about it.

I'm in my late 50's and the gentlemen tenor who sings next to me is 81 and so we developed a kind of system where if we both need to take a breath at least we try not to breath at the same place in the musical score unless of course it's called for. The majority of our choir consist of those aging singers, God love them all, who still come and commit the time, so I cut him a little break. I will be doing well when I hit my 80's if the younger man or woman next to me cut's me a break.

Before one worries too much about commas, perhaps one should first learn to use apostrophes correctly.

(Is there a reason why I keep reading this thread title as "comas in music text"? No, there shouldn't be any comas.)

To Gavin's comment above: I think in this particular instance we have a case of conditioned breathing on account of (some) (pre-conciliar) organists taking this hymn (I presume the tune is LAMBILLOTTE?) at a pace of roughly 'quarter = 20', necessitating a breath after ev'ry four notes:

Come, Holy Gho----st, [gasp!] Crreeatorrrr Ble----st, [gasp] ... &c.

Before one worries too much about commas, perhaps one should first learn to use apostrophes correctly.

Corrected!

LAMBILOTTE is meh.

There are other important organ hymn playing techniques to be mastered before one begins playing the commas. But you know that.

A particularly felicitous use of commas in Isaac Watt's incomparable hymn on the last line:

Love so amazing, so divine, demands my soul (COMMA) my life (COMMA) my all.

https://www.youtube.com/watch?v=j5dEQMMa_pY

I am not an organist. However, they frequently annoy me. Ergo, I have opinions on how they can annoy me less.

A comma, or really any breath, should not (in metrical musical) interrupt the flow of the beat.
The time spent breathing or pausing or whatnot either needs to be taken out of an existing beat, or added in as additional beats using whole multiples of the existing beat.

Nothing kills a tempo quite like the addition of multiple pauses of indeterminate length.