I say yes and no.
My club is has 2 courses that are very different. A Pete Dye links course and a tight hilly parkland style. An 80 at Dye puts me sub 10 HC. An 80 at the other puts me over 10 HC. I make an effort to play other courses about twice a month. I have found that courses that resemble one of my 2 courses I can play at or near my HC. When I say resemble, I mean similar greens, terrain and conditions. It's encouraging to play my "hard" course often so when I play a "normal" course I can score well.
BUT, if a play an easy flat goat ranch I will always be well over my HC because the rating/slope are so low I'm already giving 5 strokes and then course conditions are so poor that greens don't putt true and hardpan fairways make shots tougher.
Similarly my parents belong to a club in the NC mountains. Very high slope rating with unreal elevation changes. Never a flat lie, everything is uphill/downhill/sidehill. Lots of false front greens and sand all over. Miss a fairway and it's stroke/distance. Reading the greens in the mountains is like being in a fun house where nothing looks like it is. Sand conditions are totally different than the Midwest and when it's wet it's even tougher. Figuring out the club on a 175yrd par 3 that drops 120ft is daunting and add a little wind and you just pray. Uphill green shots are just as bad. I dread the member guest because I can't even come close to playing my HC. I've played it probably 12-15 times and the best I'll manage is about an 82-85.
I can go to my brothers courses in Charlotte and score just fine because they are so similar to mine. Going from bent to Bermuda isn't an issue because the terrain is so similar.
If you ask me, the guy that carries a handicap playing poor conditioned variety of courses will kick the tar out of the same HC that plays the same, well manicured course.