Theoretically, if you could provide the TBI with an adequate supply of fuel, then it shouldn't matter what type of pump you use. The problems are that:
1) Most mechanical pumps do not provide enough pressure to feed EFI. TBI only requires 15+ PSI, depending on year and setup, but most mechanical pumps only provide 5-10 PSI.
2) More importantly, most mechanical pumps provide fuel in a surging manner as they pump.
That being said, there are Mechanical pumps that provide enough PSI. There is a new design (as well as some older ones) on the market that can provide 50+ PSI, but I'm not sure about the surging issue. I would like to experiment with said pump and a good regulator on a TBI system to see if it can provide adequate and steady flow. Ideally, I would like to install a mechanically fed TBI system on my 80, along with a large cap HEI, so that I can bolt my Q-jet back on if I'm in the sticks and have issues with my EFI. That and it would make conversion much easier if I didn't have to deal with any fuel system upgrades and or return lines.