2009 MacBook Air: I can, and want to, purchase an SSD upgrade, but what about Mavericks > Sierra?
Replaicing your rather slow spinning HD with an SSD will certainly make your Mac faster. In fact its the one upgrade that will give you a noticeable speed bump. Other things can give you some speed like RAM (not an option for you) but the SSD is a great upgrade.

That said Apple does not support upgrading to Sierra (though there are hacks that will allow you to do so, which is beyond the scope of this site.)

The only way to see if it is to slow for your intended usage is to try it and see. Personally, 2gb of RAM is considered pretty small these days and I would be hesitant to upgrade the OS because of that. But depending on your use case it might be acceptible with the addition of an SSD which should speed things up considerably.