This is a perfectly valid scheme from a mathematical point of view, and here’s why. It all has to do with the memorylessness of the exponential distribution used by TagTime. Since it is memoryless, the expected ping distribution is the same on any subset of time. So imagine simply “deleting” the ten minutes spent manually tracking (and ignoring any pings), that is, imagine that from TagTime’s point of view time simply skips ahead ten minutes. Since the distribution is memoryless, TagTime cannot tell the difference at all. That is, the expected distribution of pings that happens after this skip is exactly the same as it would have been without the skip. So if you manually track time on some interval and ignore any pings, TagTime is still accurately tracking you on everything outside that interval.
As others have pointed out, the one important point is that once you start the manual timer you have to commit to not counting any pings you get, until you have decided you are done manually timing. For example, you cannot start the timer and then as soon as you get a ping, stop the timer, submit the manually timed portion so far, and also count the ping.