The problem is that unless the shirt is specifically PFD (Prepared For Dye), you could end up with contrast stitching (the thread is polyester, the shirt is cotton, the dye only works on cotton) and/or major shrinkage issues.
It won't affect the ink when you come to print, assuming the shirts are fixed properly after dying.
All in all? Way more trouble than it's worth, especially as a money saving exercise. Custom dying isn't something I'd contemplate unless you were trying to match a specific colour.
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