Usually yes Barry. The other aircraft would indeed also receive an RA, and in most western companies that RA will take priority over any ATC instructions.
However, if the other aircraft has no TCAS (fortunately more and more rare nowadays), but only a mode-C transponder? 'Our' aircraft will create an RA based on the current vertical behaviour of the other aircraft. If ATC now issues an instruction to the other aircraft opposite to what it was doing it could at least cause a problem with the RA instruction. It may be revised to a more aggressive manouvre, or of course it could be worse...