To be honest, the biggest motivation for me, is the visa sponsorship.
I think it would be a mistake - you want to use this as an opportunity to make the case as to why you want to work for this company and "well, I'm in it for the Visa" isn't particularly appealing. In much the same way as going to a singles event and saying "I'd love to marry you.....for a green card!" is unlikely to work out well.
It basically infers that you don't care who you work for so long as you get the visa, and most people would prefer to hire someone who actually wants the job, there's likely to be no shortage of candidates who would want the job itself (regardless of whether they need a visa or not) and they are going to be no-brainer picks over you if you say that.
So try and come up with some reasons why you want the job that aren't the visa and use those in your cover letter instead. If you can't then I'd suggest doing both yourself and the employer a favor and moving on.