A bad control arm actually does both - it's not really an either-or situation. The alignment will definitely be off, but more importantly, a worn ball joint or bent control arm compromises the entire steering geometry and can make your wheel feel exactly like what you're describing: loose and unpredictable when turning. That vague steering feel is your car telling you something's wrong with suspension geometry, not just a toe-in issue that an alignment shop can fix.
You should absolutely have this inspected before putting many more miles on it. A failing control arm doesn't just make your car uncomfortable to drive - it can affect braking stability and emergency steering response when you need it most. I learned this the hard way years back when I was out on a frozen lake and my truck started pulling weird; turned out to be a control arm that had been getting progressively worse. Take it to a shop and have them do a full suspension inspection under the vehicle. They'll look for play in the ball joints, bent arms, or worn bushings. It's a quick check and way cheaper than ignoring it until something gives way.