and that visible gap would look horrendous, since you lay the thinset, slide in the tile, then push down to adhere properly. Spend a few extra minutes and do it right. If you want the baseboards to match, get a shorter style, or trim the bottom of the base with a table saw.I don't do tile, but I'd assume it might be harder to fit the tile evenly under the base board than just remove it then reinstall it on top.
Yes, I TRY to reuse, but in many cases I end up with new since the old ones break as you remove them. The height difference from room to room is not usually noticeable unless they touch directly.Welcome to the site. You mean replace as installing brand new baseboards?