I think it's worth an answer. Is sort of game specific but not really.
I assume many runners on cart-based systems use flashcarts where the original is expensive. Would effectively be the same as a reproduction cart. Main difference (only difference?) from real battery-backed save cart is saving and loading operations are much faster on flash memory. Flashcart has unfair advantage where saving is required. No saving? I doubt it's detectable that you used it.
Isn't that basically an emulator? And emulators are absolutely a game-by-game sort of thing.
This is a pretty interesting question. As far as I can tell most game community do not care or ask and there's most likely runners doing runs on repro / flashcarts
But theoretically For reproduction cart specifically as long as the chips on the cart are the same type (including special chips such as SA-1 SuperFX etc ) and the ROM flashed on it was a proper unmodified dump then it most likely does not really matter, different PCB layouts and EEPROM chips could in theory induce some difference, but not to any game changing degree, save RAM mods could have an effect on anything that tries to access it (Not to mention some of those require a modded game to work), the real issue is whether what's on the cart itself is the clean unadulterated game version you think it is, dunno specifically about multigame carts but would guess it has a higher chance of behaving differently from the original carts. For flashcart it's more complex, the flashcart itself has to emulate the behavior of an actual cart, and unfortunately cart aren't usually simple storage for the game , there's mappers, special chips, save SRAM (some games use it for more than saves, specifically RNG). For mappers it usually doesn't matter as any inaccuracy would translate into the game not being able to access parts of it's data and would most likely break things in the process, some mappers do have additional function within the games though and I'm not qualified enough to say whether inaccuracy in said mappers could translate into hidden speedrun impacting issues. For special chips, it's emulated (except that one SNES flashcart where you could cannibalize a DSP-1, maybe there others but I'm not aware of those), and iirc there's accuracy trade-offs as the FPGA present on flashcarts simply isn't good enough to do it accurately (might have changed, but that was true at the time where SuperFX and SA-1 support on SD2SNES was unofficial) not to mention that this emulation is based on current reverse engineering efforts and while they're extremely thorough and accurate there's definitely still the possibility for some inaccuracy to have slipped by. Potentially also and I think more so in flashcarts for more modern systems the flashcart could simply have faster (or slower) read speed compared to regular carts (I don't think they cache the ROM to SRAM like flashcarts for older system do)
tl;dr: repro shouldn't be an issue as long as you're sure the ROM is the right one but flashcarts can definitely deviate from the original game behavior although they won't in most cases.
PS: Obviously not accounting for people who would intentionally try to cheat in a way only a flashcart / repro could allow easily.