I've done a few covers in my life...good fun but I wouldn't recomend making it a habit of it. I have noticed that some people start writing a song and get frustrated with it and just end up doing a cover instead because they want to record SOMETHING. Maybe, just taking a step away from music for a day or two is all you need. Often at the frustration point, I come back a few days later, and say what was I thinking, that was pretty cool...or only have a few changes to make to make it great. I don't know if it will mess up your technique. It might be more the result than the cause. Not enough imagination to write a song, so the person just covers a ton of songs because they have a certain level of musical competency, but not really any ideas when it comes to songwriting.
The occasional cover is okay, but people generally start to wonder if you do a ton anyway.... unless you want to play weddings and corporate events (those guys do make a bunch of money... but..hmmm... NO!).
Instead of approaching it as learning songs, which probably will make you unconciously write parts that are identical that you might even think you came up with, just listen to a lot of different kinds of music, deconstruct it and figure out what approach is used, rather than just strictly the notes. What approach is behind the notes that make it work, not really the notes or chords themselves.
One thing that is cool, try to write a song with a performer on an instrument that you have no idea how to play. You can bet, after all the frustration and head pounding is over, it won't sound so much like what is typically played by that instrument. But then again, I love situations like that... bringing gothrock players in on industrial records, death metal guys to play tracks on ambient, etc... keeps things interesting and quite chaotic. YAY!