Will botox for gummy smile lengthen my upper lip at rest?

Thank you for sharing your question and photographs.  Botox placed for a gummy smile will not impact your upper lip length at rest.  Hope this helps.

Thank you for supplying photos, but unfortunately they are not at standardized angles for proper examination. Botox may be used for a Gummy Smile. Botox is used to relax the muscle and inhibit strong movements. Therefore, a Gummy Smile Botox treatment will NOT lengthen the lip in any way while its at rest. It will only reduce it's sharp movements upward when you smile fully. If seeking potential treatment, I strongly recommend that you follow up with an experienced injector, preferably a Facial Plastics Surgeon.
Keep smiling! 
Best, 
Dr. Anil Shah

Botox is a neuromodulator that works by relaxing facial muscles to reduce the appearance of a gummy smile. The effect is restricted to facial movements, which means when your lip is in a resting position, you should not see any difference. The medication will only restrict your lip from pulling up when you smile - it will not lengthen the upper lip in any way. 
From your photo, it appears you might benefit from a combination of Botox to reduce the gummy smile and dermal fillers to increase fullness in the upper lip. I recommend you schedule a consultation with a board-certified dermatologist with expertise in this treatment. With the right provider, you could achieve very satisfying results.