Does the EZ-4 support Real Time Clock games?
Assuming you mean GBA RTC games, no, it doesn't. You would have to patch Pokemon to run w/o the clock; there is an IPS patch out there that I can't be bothered to look for now but Google should be able to help you find it. DS games obviously use the DS in-built clock.
I must caution you though, if this is your criteria for how well the EZ4 handles GBA games vs the Super Card and GBA support is that imprtant to your friend, they had better do some more homework before they buy the Super Card or they may find themself dissappointed. I'm not trying to trash talk the SC, I don't own one, but from what I've read GBA support is not one of its strong points (ie the naff way saves are handled, and if Takaishi is right slowdowns). Barring the RTC, GBA support in my experience on the EZ4 is flawless.
As others have mentioned, the M3 may also be a good choice for your friend, but it doesn't meet the "cheap" part of your friend is looking for. There are a million "which cart should I get" threads, reviews, etc. Read up, and decide which is best for you.