Can I Get Veneers if I Have a Lot of Cavities and Need Root Canals?

In the case that you are describing, the first thing that should be completed are any root canals that are necessary.  Once they are completed and the decay is removed, your dentist can assess how much good tooth structure is left.  That would determine whether you would have veneers or crowns as your final restorations.  Based on what you are describing, my guess would be that your dentist would place all porcelain crowns on these teeth.  This approach would protect the compromised teeth and give a great aesthetic result.  Good luck.

If you haven't treated the root canals yet, then that's first on the list. After they are done then the tooth is evaluated to see how much good tooth is left. Then the dentist chooses the crown or the veneer to cover the dead tooth. The tooth will darken over time so covering it is usually necessary.
Dr Thomas

If your teeth have a lot of decay, root canals, etc, your treatment plan may consist of a combination of veneers, 3/4 crowns, crowns and/or onlays. All are porcelain restorations that -- when done properly -- will look good, feel good, and should last a long time.

If you have large amounts of decay, cracks, chips, root canal treated teeth, etc then full coverage crowns are more likely. A veneer is simply the front half of a crown, so if a tooth is damaged to the point that the back half is in need of attention, then a planned veneer becomes a crown.
If the desired goal is a smile rejuvenation or makeover, a combination of veneers and crowns is common. Sometimes the entire treatment is use of crowns, but the appearance is the same.