No. Pets are companion animals - that is, they are kept for their companionship and for personal enjoyment. Though it is entirely feasible for me to "study" my pets and learn about their behaviours while I keep them. any form of "study" associated with the animal is secondary to the companionship.
By contrast, a laboratory animal is kept specifically for scientific purposes, and this distinction makes a significant difference. While care requirements may be very similar, the scientific purpose will, almost by definition, seek to vary some aspect of the animal's care in order to test the change in behaviour. This might be to the detriment of the individual animal's health or welfare while still being in the best interests of the species.
This is entirely at odds with keeping a pet where concern for the individual animal's welfare is paramount.