> Wouldn't that make things worse? Those applications usually expect to be able to make these calls. So now, instead of lagging once in a while when the home base is having troubles, it will lag all the time.

Not necessarily. The lag may be waiting for the remote server to respond to a request, and the app may move on quickly if it can't open a connection at all. It's not totally uncommon to work totally offline (e.g. on an airplane), so there's a decent chance the test that scenario.

In my experience, each time a firewall is blocking a connection, you experience it as a timeout, so the app tries to connect and finally times out.

Which would take longer. I haven't tried though

No, it usually results in an immediate connection refused.

it won't wait for a timeout if the connection is explicitly dropped by a blocking rule

It depends entirely on how the firewall is set up.

If you are getting timeouts then the folks who set up the firewall hate you.

It can be the case that an immediate, explicit failure is faster than waiting for success (or worse, timing out).

It shouldn't, because any network requests would fail early and instantly, somewhere around opening the socket.