ATTQOTD: I probably wouldn't recommend someone start speedwork in their first few months of running. You're less likely to get injured if you give your body a chance to adapt to running slowly before you start running fast. Plus, when you start out, you're probably running too fast in general, so you're sort of doing speedwork all the time. If you add actual speedwork on top of that, that's more injury/overtraining risk.
But after you've been running consistently for a while and you're comfortable with it? Sure. Speedwork is great. It will help you get faster - and you're allowed to want to get faster regardless of whether you're at the front or back of the pack.