Direct to garment is a digital print. If you do not have the specific CMYK profiles it is recomended that you send the file in RGB with R0G0B0 values as black.
A lot of people think that a CMYK output is a must when sending to print. It is not. Sometimes you need to avoid it.
It is a must when sending it to a CMYK separation, like offset print or color selection silk print.
But on a digital output (unless you have total control on the rip) you need the rip decide the separation of colors. Some printers can use 6 inks, some use diferent color profiles, some will have some built in tweeks to make your print "pop", etc.
If you have the same design going for print, web, and fabric, do you have separate source files having the specific colour profiles?
Interesting one. Yes.
You should understand what a color profile is.
It is a series of "matrixes" to adjust colors depending on the conditions, to be printed or viewed. Ink types, brands and surface to be printed.
Coated paper, office paper, newspaper, cotton fabric, sinthetic fabric, silk print, offset print, sublimation, inkjet print. Japaneese inks, german inks, north american inks. Transparent inks, opaque inks. 6 color separations... a big etc.
So the answer is yes at some extent.
At least you need a sRGB rgb profile for web, or drop the profile completly. The CMYK profile is only to see the colors somehow similar to a print, but on an RGB file is not stored.
On a digital oputput you could use either Adobe 1998, ProPhoto RGB or sRGB.
On a real CMYK output you need at least a standard profile depending on your region and basic paper type. (Swop, Gracol, Fogra, Japan Standard)