No… not veneer.
She may be assuming you only want to refinish the top…or she may be looking at using something like Formby’s, that doesn’t fully strip the finish.
She stopped by today, and I could tell she was experienced. She looked the table over completely (legs included), noting some areas that would be obviously more difficult to treat than others. She did up her price to $200 when she saw these areas along the side of the table top that are slightly curved (more detail). I asked her about the process, and what she described is exactly what everyone here suggested… strip, then sand; 2-3 coats of varnish, and ‘sanding’ it with steel wool in between coats. She feels the imperfections that are on the table now are due to not doing the extra ‘sanding’ (whether you use sandpaper or steel wool) in between coats of varnish when my mom had it refinished a number of years ago. She will also take a chair with her so when it’s time to match a stain, she will have the chair to match against.
She was born in Oklahoma, but raised in Venezuela. They moved to our area when her husband got a job here. She has a new baby at home, and this is one of her hobbies she does when the baby is sleeping. She is also a painter. She will be picking the piece up in about three weeks, when she’s done with a couple of other pieces she’s working on.
Wow. Amazing. Good luck!!
(And then when she’s done with that, I have a couple of pieces she can tackle.)
I always used very fine steel wool in between coats of varnish. Worked well.
Sounds like she knows what she is doing. Is she insured?
It was funny… when she was describing the process and she got to the part where she was going to tell me about the ‘sanding’ between coats, she hesitated and told me, “Yes, between the coats - the metal - I can’t remember the English word - I use it between varnish coats.” And I said, “Steel wool?” And she smiled and said, “Yes, that’s it.”
Good job doing your homework first with the CC professionals, @teriwtt 
Sounds like she knows what she is doing. I hope she keeps her baby away from the smells and chemicals of the process!!! Let us know how it turns out.