If my veneers were not done properly, meaning there was a slight gap between the veneer and gum would this cause a cavity?

Yes, any restoration that is not sealing correctly will very likely give you
problems in the future this problem can be: increase of sensitivity cause by
dentin exposure, accumulation of bacteria for the millimetric gap (not an easy access
to clean well) and therefor possible cavity formation.
Please
make sure you have this problem fixed as soon as possible and, in the meanwhile
be extra careful with your brushing and hygiene technique.

It is unlikely, but yes it is possible depending on how long ago the veneers were done and your home care routine and brushing technique.  If you are not brushing well at the gumline, debris and plaque can remain and cause decay.  Keep in mind however that cavities do not develop overnight, it takes time.