In bitcoins, it is possible to check if a private key is valid using the WIF checksum.
Is this also the case for altcoins which use SHA256. And how about the ones that use another hashing algorithm?
How altcoin wallets import private keys is up to the specific altcoin, so I cannot provide a blanket answer for all of them.
However, I can tell you that this functionality is not determined by the hashing algorithm used for the altcoin's proof-of-work. That is independent of the Wallet Import Format, which just so happens to use SHA256, and does not use SHA256 because that is what Bitcoin uses for proof-of-work.
My guess is that most altcoin's (but not all) support their own version of WIF, but with a couple of likely differences.
First, the altcoin may not use the same asymmetric cryptography for creating addresses, which means that private keys might not be the same length as they are in Bitcoin. Since the private key is the input of WIF, this can have a consequence on the end result.
Second most altcoins will probably use a different network identifier that gets pre-pended to the private key in step 2. Bitcoin's mainnet uses
0x80, but an altcoin could use whatever value the creator felt like. Perhaps it was changed...perhaps is wasn't.
Other than that, I would guess that most Bitcoin-clone altcoins use the same process for importing private keys. It is also possible that the checksum is created using a different hashing algorithm than SHA256, but that algorithm in no way has to correspond with the proof-of-work hashing algorithm of the altcoin.
Check the docs on the altcoin in question to find out for sure.