Not necessarily. Mainsprings break typically in 2 locations on the spring. One is in at the barrel arbor, so like this:
View attachment 1032006
If it breaks near the inner coil as shown above, the watch will stop running. However if it breaks at the other end of the spring, where the welded tang is that anchors the spring to the barrel, it will continue to run, and often they run quite well, and the power reserve may drop only by a couple of hours. The spring will slip when you wind it, so it will never stop winding when you turn the crown.
Again, as I said, this would be unusual right after a service, provided that your watchmaker replaced the mainspring with a new one, which is standard practice. If they used the old spring again, then the chances of there being a problem go up.
The way to find out without any additional speculation is to simply wind the watch until it stops...you don't have to wait until tomorrow morning, as you won't hurt it winding it now and then again tomorrow.
Cheers, Al
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