No, there is a lot more to it than that.
Anti-A and anti-B are isoantibodies, rather than alloantibodies. In other words, they are "naturally occurring" and do not have to be stimulated by either red cell transfusion or pregnancy. They are usually stimulated by particles in the air (including human cells that have been shed into the air) that either express chemical compounds that mimic the A and/or B antigens or, in the case of shed human cells, actually do express these antigens (remember, the A, B and H antigens are histoantigens).
On the other hand, genuine alloantibodies (for example, let's say an anti-Jka) that are stimulated by transfusions and/or pregnancy, have, by definition, shown the individual to be a "responder". It is by no means unusual for an individual who has produced a genuine alloantibody (such as the anti-Jka mentioned above) to produce an alloantibody of another specificity (or alloantibodies of other specificities). Such other alloantibodies may not be easily detectable by routine serological techniques for various reasons. Three of these are that the antibodies may not become serologically detectable at the same time (one may be detectable as early as the other, as not all antibodies "read the books"), that an antibody may be evanescent (or "disappears" from the circulation quite quickly - such as many Kidd antibodies - but these can remain clinically significant if re-stimulated), and thirdly, that the cognate antigen is not expressed on either the screening red cells or the red cells used in the antibody identification panel (for example, in the UK, to give two examples, the Jsa antigen and the Wra antigen, and both of these antibodies can be exceedingly clinically significant).
For this reason, it is very important that a serological cross-match is preformed (and found to be compatible), even if the blood provided is antigen negative for a known cognate antibody.
You may well ask, "Well, what about an anti-Wra (for example) that is present as a monospecific antibody? Is that not clinically significant?", and the answer is "Yes"! Indeed, there was a fatal case of an acute transfusion reaction caused by anti-Wra within the last decade in the UK, and the court decided that it was death by misadventure, because anti-Wra is known to be quite a common antibody, whereas the cognate antigen is sufficiently rare for the Law to recognise that it does not need to be expressed on screening cells (otherwise the Reference Laboratories would be overwhelmed with samples that have anti-Wra in their plasma/serum - and this is only one such specificity). This may be one of the few times that our judiciary have used their brains (did I say that??????????!!!!!!!!!!!!!!!!!) and the decision may have been influenced by an editorial in Transfusion, written by the late, great Professor George Garratty (Garratty G. How concerned should we be about missing antibodies to low incidence antigens? Transfusion 2003; 43(7): 844-847. DOI: 10.1046/j.1537-2995.2003.00492.x.).
SORRY THIS IS A BIT (VERY) LENGTHY!