Could a varicocelectemy cause hair loss due to the rapid rise in testosterone?

Yes, this may increase hair loss. I suggest seeing a hair loss expert now to evaluate and go over your condition and provide you information about your best treatment options. There are great non-invasive options like prp/progesterone and/or hair transplantation. See an expert. Best, Dr. Emer

Recent Studies have shown that men who have had varicocele repair  had an increase from low testosterone to normal testosterone. In my opinion, It is more likely that the procedure itself caused a telogen effluvium hair loss or acceleration of male pattern hair loss. Visit a hair loss expert and develop a definitive diagnosis and treatment plan.

Testosterone levels may or may not change after varicocelectomy. Studies have shown that with varicocelectomy involving less than 5 veins for example there were no changes in serum testosterone. With men having procedures involving 15 or more veins, there was a slight rise in testosterone. However, these levels were still within the normal physiological range. There are many reasons for hair loss and one should always get a proper assessment. Changes in serum testosterone are not typically responsible. 

The stress from ANY surgery can cause a temporary shedding.  This type of surgery doesn't usually cause the rapid and significant rise in testorsterone that would be associated with hair loss though.  You might have other causes for hair loss - check in with your hair loss specialist.
Good Luck!

Any surgery that causes stress, can cause an acceleration of hair loss in individuals with genetic hair loss