I am only familiar with this in the context of RPMI cell culture medium. It should be okay since the tris is diluted out. I would only be wary of the potential affect of tris on the pH of the culture and at the temperature you intend to culture at.
Dear Natalie, I think, you do not need to dialyse TBS, because it is non-toxic to cells and formulated as isotonic solution. As a rule, you can add in in vitro cultures up to 10-15% (v/v) of isotonic solution (NaCl saline,TBS or PBS) not affecting cell survival. Anyway, I would provide the control wells containing the buffer in corresponding dilution.