I will be using Minoxidil for a short time, but will my hair fall start again once I discontinue use?

First, it would be important to gain clarity on what type of hair loss you are experiencing. A doctor who specializes in hair loss would be able to diagnose your condition. It would be important to know whether you are being affected by pattern baldness, telogen effluvium or other culprits like medication side effects. Hair regrowth may be possible if the hair follicles are only experiencing a temporary resting phase. If your condition is due to genetic pattern baldness, hair transplantation would be the most reliable approach to recover your desired coverage. Learn more about hair restoration for younger patients in the article link below.

It is important to remember that gains made while using medical therapy such as Minoxidil are dependent upon continued use. Cessation of therapy is typically associated with some loss.
With regards to your specific, the cessation of medical therapy is often accompanied by the loss of the gains which are attributed to this therapy. However, the losses are typically limited to the gains made during long term usage (4-6 months). This due to the fact that it takes some time for the development of new growth which is medication dependent.
As always, discuss your concerns with a board certified plastic surgeon (ABPS) with experience in hair restoration.

if you get regrowth from using Minoxidil once you cease use of it you will begin to lose the new hair you gained from using it.

 If you developed minoxidil dependent hair and yo stop the minoxidil for more than 3 weeks, you can lose these dependent hairs. It takes time to develop dependencies.