Hmmm, yes, sort of, but it would involve a considerable amount of work and learning how to use font creation software (there’s a learning curve). Text with every first letter of every word set in a different weight of type would be sort of ugly and weird, but I guess you have your reasons.
You might ask your question on TypeDrawer.com. There are lots of type designers there who are good at figuring out this kind of thing, but I’m sort of thinking that there’s no easy way to do it. OpenType fonts support a certain amount of programming, so there might be a way by adding medium-weight alternates in the font.
An easier way might be automating something within whatever application you’re using. If it’s InDesign, regular expressions (a text manipulation language based around pattern recognition) could likely handle it.
Unless you really need to do this for some compelling reason, I’d probably advise you not to pursue it.