I mean, yes and no:
If you import an address that was created using a different scheme, then the wallet will honour that scheme and it will internally use it for everything. It has to, because using a different scheme would produce a different public key. So, if the wallet is able to successfully import the address, then it has to honour the scheme that it was used for the account which is being imported.
On the other hand, AFAIK wallets in this ecosystem, in their UI for creating a new account, don’t allow the user to pick the underlying signature scheme. They could, but I think (don’t quote me on this, I have not tried them all) that they don’t. Probably because the signature scheme is deemed as an implementation detail, and wallets try to make the UX simpler for users. In other words: why confuse the user if there is no need to?
For instance, this is -roughly speaking- what happens when you create a new “account” using the PJS extension:
- The extension generates a 12 word nemonic seed phrase that the user should write down, remember, keep safe, whatever…
- It then hashes that key-phrase so that it deterministically produces a private key.
- This private key could be used with different signature schemes, but doing so would produce different public addresses.
- In order to avoid overwhelming the user with unnecessary options/permutations, the wallet uses a default signature scheme. In the case of the PJS extension that is
sr25519.
However, if you are an advanced user and you wanted to add a new account using a different scheme, then you could do that by using the option “Restore Account from backup JSON file” and in that json file you could specify your preferred scheme. I mean, I guess that I don’t see why anyone would want to do that unless they are actually importing an account from somewhere else, but I mean, you could do that.
You could also fork the PJS extension and add the option of picking a different signature scheme, I guess, but again: I have a hard time understanding your use case.
What happens with Ledger and other hardware wallets?
Ledger and other hardware wallets don’t ever “leak” the private key outside of their hardware device. That’s why they are a lot safer than hot wallets. When you use a hardware wallet through a hot-wallet (like using ledger via the PJS wallet), it’s the hardware wallet itself the one signing the transactions, and all what the browser extension does is to provide a UX so that the dApp can communicate with the hardware wallet.