Depending on the type of accelerator and the amount of accelerator used yes accelerator can compromise the bond. Typically accelerator shocks the CA into curing causing a more brittle joint. In some case the CA can be shocked so violently that it will actually foam up introducing air into the joint. Accelerator should never be used with thin CA and there are times, if used properly (like making fillets or filling gaps) it is perfectly acceptable to use accelerator. If accelerator is used always use it sparingly.
Mercury Adhesives accelerator has been formulated to be a bit less aggressive so as to not shock the CA but simply speed up the set time needed. The most common use for accelerators is to help with hard to bond substrates.