Considering my 27.2 Thomson slips a little in a frame designed for a 27.2mm post, no!
I’ve seen a 27.0 used at a push in a frame designed for a 27.2 post, the seatclamp had to be tightened loads, and it still slipped a bit. A 26.8 post will have no chance of staying where it’s supposed to!
Theres a good chance you’ll end up damaging the frame over time too. For the sake of the frame get a new seatpost. Have a look on the clasifieds, theres usually plenty of 27.2mm seatposts for sale on there.