A full udder/being in milk has nothing to do with being able to conceive or coming into season (urban myth, same as in humans...). You can safely milk her for the first three months of pregnancy as long as she is being fed well (but not extra). Then dry her off in the last two months, and usually that is easiest in December/January as it coincides with their natural drying off period (very low daylight hours). It is also easier to dry them of by reducing the quantiity of milk you take, so only make the udder comnfortably soft, not strip out, then reduce times of milking, and she will slowly stop to produce milk.
It is also important to track how often she comes into season (it should be very three weeks) - she will tell you when she is! Unless she is a) already in kid after making her own arrangements (you should be able to smell if she has been with the boy) or b) she has gone cystic, in which case you will be having real difficulty in getting her to hold to service. She will be in season regularly from anything like every 5 to 10 days - again you will know. If that is the case, vet may try some injections, but I have only rarely heard that they are successful.
If she is not vocal when in season, I would take her next to the male's pen once a day for the next three weeks - she will wagg her tail and actually run up to him when ready to be mated. Her backend should also be pink and damp. He may be keen all the time, but unless she is too, you are just be wasting his energy.
For the vet visit on Tuesday I would ask him/her to bring a scanner to check for pregnancy and I think she can also get a blood test done (I guess you are taking bloods for CAE and/or Johne's anyway). I am however uncertain if a blood test can distuingish between a phantom and a real pregnancy - vet should know. You can also get a pregnancy test done through the milk, but you would have to contact your local NMR lab.
If she did have a previous unsuccessful pregnancy or abortion, she may well have gone infertile as a result of that, or in rare cases she could have a mummified foetus still inside. Scan should tell you.
However tbh, if she cannot conceive naturally you are better off ing buying another female rather than spending huge amounts of cash on what is unlikely to be a successful outcome, given you don't know her past history and have to rely on whatever the seller told you.... Unless she is pedigree (and then again of a rare and high quality) you may well have to ckalk this one up to experience.