Vector and pixel art are completely different things. Your question mentions both.
Like any art, you would learn from the ground up regardless of your background. Art is art. If a 3 year old can create art you can. There's not really much to learn to "create art". The learning curve comes in when you want to create artwork for a specific purpose.
You didn't go into any detail. Your question is a bit like "can I learn to cook coming from a butcher's background." One has nothing to do with the other and learning to cook for a Michelin star restaurant is a great deal different than learning to cook for your children.
If your goal is to learn to create vector art, you would find a vector application which you enjoy using and start learning about how to use that application. The same would hold true for pixel art.
The only important aspect would be to choose the proper application based on your desired final output. For example, Photoshop does not create true vector files. Regardless of anything you find about "creating vectors in Photoshop" you can not use Photoshop if your goal is to end up with a truly vector file. You need apps such as Illustrator, Xara, CorelDraw, etc.
For pixel art, Photoshop works as does any of hundred other pixel-based editing applications.