Yes. And it should be pretty small. My wild guess is a few tenths, tops, with a decent load running (like +25A). With a decent load it won't be zero. It can't be, because the bimetallic strip inside the breaker has to heat up to work. And that creates a little voltage drop. Note that the typical DMM is not going to be really great at measuring small voltages like that. But...
In the OPs case, presuming the loose connection was one one side of the main only, you can measure the FOP (voltage drop literally from top to bottom of the main) on each pole of the main breaker. Even if the DMM is not super accurate, it will very likely be able to tell you a good side from a bad side. If one side shows 0.2V and the other shows 2.7V (with mostly same amount of current on each leg), then like the saying goes... "There's your problem".