You've got the gist of it correct, yes. Your change will be "almost instantly" propagated within the constraint of whatever the TTL on your host record was before the change, but it's almost certainly way lower than the standard 48-hour TTL on the records that your registrar pushes to the root servers. For example, right now your host records have a TTL of 900 (seconds, = 15 mins).
You should have the right to point any resource that's legitimately under your control, to any other resource that's similarly yours. Whether mt actually honors that for their DNS service, I couldn't say; I'm a fan of using a 3rd-party DNS service (neither part of your registrar nor your hosting provider) to avoid that kind of problem, among others.