I live in Japan.
There are collectors here who do go after American cards of US players who came over here but since most of them for guys like Rhodes are from the junk wax era (and since the market isn't that big) I doubt it moves prices.
I just found a copy of that 91 Upper Deck card you mention for sale on Yahoo Japan Auctions (Japan's version of Ebay) with a BIN price of 300 Yen (about US $2.50) here:
https://page.auctions.yahoo.co.jp/jp/auction/j461165778
As with Ebay though BIN prices for stuff like that aren't indicative of actual market price, here is another auction for a lot of 68 MLB cards of US players who played in Japan with a 500 Yen starting bid (about US $4) and no takers:
https://page.auctions.yahoo.co.jp/jp/auction/q280075691
About 15 years ago the cards of Randy Bass from the early 80s, which are commons in the US, used to sell for a premium here, but these days that seems to have dried up. Japanese collectors are now wise to the fact that US cards from the 80s and 90s are basically worthless.
With Randy Bass, his Japanese cards from the 80s are quite valuable (the 80s in Japan was not a junk era and the Calbee sets from that decade are extremely hard to put together). For Rhodes though even his Japanese cards sell for the same price as commons despite his impressive career here (also he played here in the 2000s, which is kind of the Japanese version of the junk wax era). He played mostly for Kintetsu, which isn't a super popular team (in contrast to Bass who played for the popular Tigers and is still a legend here. Warren Cromartie played for the popular Giants and his Japanese cards also sell well).