let me put it this way; I would recommend the multi tool over the dremel attachment for this use. Some guys will only do it with hand tools even today with other options, others will go grab a power tool just for the sake of a power tool.
Me personally, I have removed a few tiles with the HF blades on a HF oscillator. The world didn't end. It was loud, annoying, and my least enjoyed use of this tool. But it did the job. The remaining grout won't be pretty, there is the possibility you can go too deep (the finer/nicer the grit blade the more its likely to cut into the back board or other materials) and you can have chips of grout & tile flying every which a way. It's not like cutting wood at all with one, which is what I use mine for almost exclusively. Afterward there was still some hand tools needed to clean up the cuts some but it wasn't bad, just not very much fun.