No. I wouldn't even make it to the deities. Captain America or Batman would only make it so far. Purely physical training only takes you so far, and the same can be said of any other training regiment. Also, channeling power requires power, so a powerful artifact is limited by the power of its wielder.
Further growth is gained by tempering your will and soul against challenges that matter, with the fastest gains in raw power usually being seen in combat. But an Elementalist throwing themselves against the weight of the world to try to divert a tsunami enough to save their home village or such would also grow, assuming they survive.
While CA and Batman have gained some portion of that edge, they haven't done it in a world where gathering enough might and notoriety can make you an ageless immortal.
Come to think of it... yeah, the Captain would do well with the way immortality can happen in this world. He'd easily slip into the role of wandering hero, ever learning, growing, experiencing, and just simply enjoying life. That last bit is really important.
Batman, not so much. His, um, issues would begin to warp him. Sure, he'd probably gain supernatural shadow-based powers and stuff, but he'd become this immortal creature haunting the city, seeking out lawbreakers and evildoers. And if that city ever became abandoned, he would haunt it still, driven by what he'd made the purpose of existence. And should explorers come his way, well, the moment their curiosity caused them to enter an abandoned building, they'd be trespassers. Especially if they had to force their way in.
Anyway, back to the original point: No amount of physical training and equipment is going to get me past the likes of the various hidden, wandering immortals. The sci-fi equipment available on the more technologically advanced planets would help me more than magical gear, especially the genetic, cybernetic, and bionanonic upgrades available, but there is a breaking point. An immortal swordsman is doing anime-tier BS like cutting through the space between him and his foes thus making the distance irrelevant, etc.
Think of Bleach and the more physically oriented Bankai that don't have special rules or weird shit going on. The ice-boy captain's 'dragon form' is a good example.
