You can do anything you want, its your tiles, its your house [i gues], but remember this:
Travertine is a stone and any tiler will tell you that stone tiles will never be prefectly cut. If you go ahead and tile with no gaps, i can promise you will have some gaps anyways, cos stone tiles are not 100% straight.
Is your floor realy level? Any small imperfection can lift the tile above another and it will look crap and be very visible. If you tile with gaps its still not gana be easy to get all tiles 100% flat, so grouted gaps hides that.