Hi efisher0,
It's important to pick the way the song calls for you to pick. But if you're able to pick up and down without missing a beat, then there's no real issue.
Remember, playing music is all about feel and timing. There's no real wrong way to do something, unless you're doing something that might cause injury, which it doesn't sound like that's the case here.
You'll eventually have to learn how to pick up and down along the strings, so if you're already picking upwards and downwards on single-note riffs and licks, I think you're actually ahead of the game. It'll be fine.
Best,
Billy