That's not how TTL works. Or do you mean propagation after changing an existing RR?

It's "common" to lower a TTL in preparation for a change to an existing RR, but you need to make sure you lower it at least as long as the current TTL prior to the change. Keeping the TTL low after the change isn't beneficial unless you're planning for the possibility of reverting the change.

A low TTL on a new record will not speed propagation. Resolvers either have the new record cached or they don't. If it's cached, the TTL doesn't matter because it already has the record (propogated). If it doesn't have it cached, then it doesn't know the TTL so doesn't matter if it's 1 second or 1 month.