A low platelet count is an indication for treatment in CLL according to the NCI guidelines. However, this is only true if the cause is bone marrow suppression. There are two other fairly common causes in CLL: immune destruction (ITP) and hypersplenism (a big spleen).
The diagnosis of ITP is not easy. There is not a simple test like the Coombs test for AIHA that you can do. It is not easy to measue how long the platelets survive. Often the answer can only be determined by a bone marrow aspirate and biopsy. What you see in ITP are increased numbers of megakaryocytes (the cell that makes platelets). Thes often appear immature - their nuclei are not lobulated and there are no platelets budding off their cytoplasm.
This picture needs to be differentiated from MDS, another cause of thrombocytopenia, in which increased non-lobulating megakaryocytes may also be seen. It requires examination by an experienced pathologist who understands bone marrow - not someone whose day-to-day work is examining vasectomy specimens and breast cancer.