Not recommended yet. Times from OpenPete are not comparable to console or emulator runs, and no leaderboard recognizes it as a platform.
Things to fix
Input timing
Input is currently delegated to PsyCross and needs reworking to be made more consistent and precise.
Load times
Level load times need to be slowed down a bit and made consistent in a speedrun mode to account for slower hardware.
Feature lockout
Save states, rewind, runahead, and non-whitelisted mods (e.g. simple skins) would need locking out for a speedrun mode.
LiveSplit integration
Integration with LiveSplit for automatic and accurate timing.
But sure, you can speedrun it for funzies!