Could Invisalign correct my crowding and single tooth cross bite? (Photos)

Invisalign would be a great treatment choice for you.  However, contrary to another provider's recommendations, I recommend having the blocked out upper left premolar removed in addition to your wisdom teeth.  It appears your upper left canine is currently in a good position and your upper left molar has drifted forward blocking out the premolar.  It makes more sense to me to remove the premolar and keep the upper canine in a good relationship with the lower teeth, rather than trying to push the molars back and try to create the space for the blocked out tooth.  
I recommend having an evaluation done by an orthodontist experienced with Invisalign to help you make a decision on the best treatment plan.  I wish you the best in your journey to straighter teeth! (and I am glad to see that you are planning on getting your upper right molar fixed).  

your upper left 2nd premolar is out of arch > extraction of that tooth.
upper molars are rotated > correction of rotations.
upper first molar is carious > extraction of that > and space closing by retraction of anteriors to relieve crowding and midline set., remaining space closure by posterior protraction.
LOWER ARCH: extraction of teeth to get ideal occlusion. invisalign will work in yr case.

Invisalign can be used by an experienced dentist or orthodontist to correct your crowding and crossbite.  Even the crowded upper left premolar can be brought back into the arch with Invisalign.You appear to have a large, deep, cavity on tooth #3 which needs immediate attention or you may end up with a seriously severe infection. Please see a dentist this week to have this treated.Invisalign results vary depending on the skill and experience of the practitioner you select.  I have successfully treated cases like yours, and I encourage you to ask the dentist or orthodontist you consult with to show you before and after photos of cases they have treated which are similar to yours before making a decision on where to be treated.  Tooth #3 molar may have to be extracted, but do not have the premolar #13 removed. Your case is going to turn out great with the correct care!

Invisalign, especially when combined with Acceledent, can quickly create excellent outcomes in cases like yours.  You did a very nice job with your photos!  Proper diagnosis will help determine if teeth will need to be removed.  I do think the wisdom teeth will need to be removed.  The anterior crossbite can easily be corrected with Invisalign.  Once a proper diagnosis has been made, there are many ways to move teeth to achieve the final desired result.  Invisalign is just a tool.  Don't get stuck on any one treatment type, and get several opinions!