Just to make sure, if we set the maxspeed tag to xx mph, will it recognize mph and calculate directions with the correct estimated time?
It will depend on the service / app that you are using, but most apps will use it, yes
If no explicit maxspeed is set, all routing applications will fall back to some default depending on the road classification in OSM.
Some apps will also take current traffic into account to calculate estimated arrival time. Current traffic and stop lights might have a bigger influence on the arrival time than using the explicit maxspeed instead of a well chosen default by the app.
mph is not good units. Not all apps process it. Use kmph instead.
maxspeed is legal speed restriction imposed by signs or road rules.
If you want to give a some hint to app for speed implied by physical road state, typical traffic conditions and so on you could use maxspeed:practical.
(https://wiki.openstreetmap.org/wiki/Key:maxspeed)
And as escada stated: It depends on the application if a unit (if present) will be respected or not.
People from UK and US complained about using km in the maxspeed tag because there is not an exact conversion between the 2 units. It makes much more sense for them to map the number on the sign (and add the unit).