Yes. Giveaways and promotions are a great way to promote your music, but when you’re giving away your recording of someone else’s song, you do need to get a cover song license.
When you record a cover version of someone else’s song, the underlying song itself is still owned by someone else. Even if you only want to get your music out to fans, the owner of the song you have covered needs to give you a license and get paid royalties.
If you do want to offer free streams or downloads of a cover song, or include a cover song in that promotional CD you are giving away for free, you can use Loudr to obtain the license. It costs the same as what you would pay if you were obtaining a license for a cover song that you intended to sell. And if you do eventually decide to start selling the track instead of giving it way, you can do so under the same license you’ve already obtained.