I've said this a few times on this forum (and on few others too): I personally wouldn't train in present climate. Thing is, there are thousands of unemployed pilots fighting for few jobs on the line. Contracts are getting worse and lobbyists are trying to pass laws which will deteriorate the working conditions even more.
Even with cadetships and airline schemes I'd think long and hard before jumping on board. But most wannabes do it anyway despite wise words they're told before starting. Just like I did
My question is, if the medical examination and money is the only restraint or is there something else. (compulsory engineering degree etc.)
Some companies require a degree when hiring a first officer, some don't. Naturally if there's two in every other way identical applicants, the guy with the degree will probably get the job.