I would have phrased the question the other way around: Can a spec an with a tracking generator replace a VNA?
The short answer is : it depends
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For very basic reflection (S11) and transmission (S21) measurements, a spec an with a tracking generator and a VSWR bridge is often comparable to a VNA is terms of functionality and results.
I just (like, two weeks ago) finished a series of videos on our ZPH handheld VNA and our FPC1500 spec an, which has a tracking gen and internal bridge. I was using them both to (a) make basic antenna (S11) measurements, (b) measure cable loss, (c) perform distance to fault tests, and (d) measure filters. Quite honestly, the results for these particular tests were very comparable. [Videos are on the R&S TMF Playlist - link at bottom of post]
Now, there are many, many, many differences between spec ans and VNAs and what they can/cannot do (well or at all). But for very basic measurements, it's often possible to use either one.
Edit: here's a picture of an older HAMEG VSWR bridge - some modern spec ans with tracking generators have an internal VSWR bridge (this includes all R&S spec ans with TGs)