That's not a path well traveled, especially at banks. At good hedge funds roles are well delineated, and chances are that you'll be working hard enough at your day job that you'll have little chance to explore on your own. Policy may prevent you access to the interesting data sets (execution data and historical P&L is sensitive to reverse engineering, and market data is often subject to expensive licensing). For banks the issue is far more bureaucratic - different teams with different hiring budgets and lines of business yada yada. There are relatively few managers high enough to wall cross between back office (technology) and front office (trading) so there's a stochastic component to your success at moving internally based on what group you end up in and how well connected your MD is. It doesn't help that coders are usually the limiting reagent (and paid less than traders) so the firm's interests aren't necessarily aligned with your own.
If you're passionate about trading and coding, HFT is a great way to go. Money makers come from all backgrounds (grad/undergrad/super technical/creative coder) and you'll likely have better control over your coding/research ratio.