My native languages are Spanish and English. I studied Modern Standard Arabic in college, and biblical Hebrew in seminary (used basically Sephardi pronunciation).
As I study Modern Hebrew, I find it easier to pronounce ע and ח in the way the equivalent consonants ( ع and ح ) are pronounced in Arabic (as pharyngeal fricatives if you like to be precise) and ר as a tap rather than the uvular sound.
For a native Hebrew speaker, what might they infer from hearing a foreigner speak this way? Might it imply some political connotation? Would it just sound weird?
It would probably sound unusual since most non-native speakers can't pronounce those letters and most Israelis don't. But some Israelis of Middle Eastern origin still do pronounce the ח and the ע in the traditional way, so such pronunciation is certainly not unheard of in Israel. And I doubt anyone would think of that in political terms.