I suspect the delay in sudo is configurable: it's not there because sudo is actually doing any work checking your password, it's there to prevent attackers from trying many many combinations of passwords quickly.
If you care about that protection, then you don't want to circumvent it, but in the equally reasonable case where you don't care, then you can probably just make sudo faster.
How is it offering protection? An attacker could use this scheme as well. If the server doesn't let the user through in 0.1 s, abort and retry the connection, circumventing the delay.
If you care about that protection, then you don't want to circumvent it, but in the equally reasonable case where you don't care, then you can probably just make sudo faster.