Not automatically. The effect of departure depends on which request is pending, and the return depends on citizenship and the evidence carried. A previously smooth entry does not establish a rule, since each admission is decided separately at inspection.
Treat each admission as its own decision
TN admission requires citizenship of Canada or Mexico, a qualifying listed profession, prearranged professional employment, and temporary entry. An officer applies those requirements at each entry, regardless of prior admissions. Where a filing is pending, the officer may also see a record of it.
Arriving without knowing how the pending request interacts with re-entry leaves the professional poorly placed to answer questions. The failure mode is assuming that a previous smooth return proves the next one. Each admission is decided on its own, on the record and the documents presented that day, so a change in the underlying filing changes what the officer is looking at even though nothing about the traveller has changed.
Ask counsel three things before deciding: what the pending request legally requires, whether departure affects it, and which document would answer an officer's first question. Where the answer to any of them is uncertain, the uncertainty is the reason to wait rather than a reason to go and find out. Hypothetical example: a soil scientist who has crossed without difficulty several times assumes the pattern will hold, when the pending request is what has actually changed.