Can they do a bone marrow biopsy even if the platelets seem fine but their is signs and symptoms of chronic leukemia?

Yes/No. Bone marrow biopsy can be done in anyone provided there is a good reason to do so and it has possibility of giving useful information. Leukemia is best diagnosed with CBC first and then doing bone marrow only if there is something wrong in the peripheral blood counts(cbc).
Yes- if indicated. If your team feels it is indicated they can usually do a biopsy unless you have another bleeding disorder.