In theory no, but there is a torque required when adjusting or you risk it either slipping again, or damaging the BB? Am guessing you can adjust with screwdrivers, but ideally you would be carrying the dedicated adjustment thingymagig.
In the manual Tony linked the recommended torque is 10 - 17 Nm, that's a huge range and I'd expect that to have a reasonable margin for error.
I don't remember knowing there was a recommendation when I had my set screw EBB, I certainly never used it. With a standard length spanner, 10-17 Nm is fairly tight without hanging off the spanner like a gorilla. Maybe try it at home a couple of times with a torque wrench to get an idea of what it feels like. I wouldn't go by feel if it was a precise measure, but aim for 15 and you ought to be able to get within 20% +/-.
Re needing adjustment after 3,000 miles. That doesn't seem unusual to me, I log such things and get anything between 500 and 4,000, but usually somewhere in the middle of that. Different makes and models of chain also behave differently, all the KMC chains I've used have needed adjustment after a few hundred miles, I've assumed this was some sort of settling process rather than wear, as they then don't need it again for a long while. I don't get that with SRAM chains and it's a long while since I used Shimano.