Can the extraction of an upper back molar tooth without bone grafting that resulted in a sinus droop commonly lead to a tmj disorder?

Not really: Keeping your mouth open wide for a period of time or stretching your jaw open wide might be a trigger and the last straw in developing some tmjoint symptoms, but it would only be temporary and short lived unless you already had other predisposing factors.

Not directly : How long ago was the extraction? As it would take time for a sinus to droop. Which molar was extracted 1st, 2nd or 3rd. Typically the extraction would not lead to tmj, unless now the other teeth are making a premature contact on your lower teeth. If it was a recent extraction ; you had your mouth propped open, TMJ could temporarily ensue which usually goes away. If not, see a dawson or pankey dds.

No.. it can not: ....The procedure can not cause TMJ ... But you could have a temporary discomfort or joint inflammation/disk derranegement because of keeping your mouth wide open, ...Maybe for too long... But that it not related to actual extractioon procedure

No: No unless the patient's jaw was opened too wide during the proceedure causing trauma to the tmj.

Extraction: The extraction and sinus will not lead to tmj/tmd symptoms directly. Indirectly the opening during surgery and the change in occlusion as a result of the missing tooth can lead to symptoms of the tmj.

Extractions and TMJ: Not the extraction per se, but your having to open widely to get surgical access to the area can cause muscle or TMJ tenderness for a period immediately after the surgery but it would not likely cause a TMJ disorder to develop at a later time.

Not normally: The extraction is the only item in your question which could lead to a TMJ issue, one with the trauma from the extraction or two the loss of the tooth losing posterior support of the mandible. There are sometimes referred pains from the sinus to the tmj.

Unlikely: Unlikely. Loss of posterior dental support can in some cases contribute to TMJ