If you are on prednisone, will lupus test positive in blood work?

No correlation. Lupus test are many . Some could change with agressive therapy , but in general low dose Prednisone will not change result, even high dose Prednisone will not make a change . Some test could be positive always like the the ANA . Some may improve like complement or anti dna , but only with agressive treatmentb.
Probably. In general Prednisone will not affect the results of serologic testing for lupus. The abnormal antibodies reflect a disorganization of the immune system that is present whether you are receiving anti-inflammatories or not. Rarely, the antibody tests will turn negative when the lupus is controlled, but in that scenario you would not have symptoms and probably would not be tested for them.
Mostly yes. Depends on the dose, but antibodies are not usually completely suppressed by prednisone, though the levels may be lower than before. Doses up around 60 mg can start cutting into antibody production.