I made a warrior char, does that mean I absolutely can never join the MG?

Depends on your skills. Guild entry in Daggerfall isn't class restricted, it's skill restricted. You need minimum levels in certain skills to be eligible for membership (except Thieves Guild and Dark Brotherhood). In the case of the Mages' Guild, it's pretty much what you'd guess-- you need a certain minimum in at least two out of the six magical skills (Alteration, Destruction, Illusion, Mysticism, Restoration, Thaumaturgy) before they'll let you join. If your warrior has no training in any of those skills, he has to boost at least one of them to 22% or better first. You'll also need a second magical skill at 4%, but you've probably already got that. Every temple offers training to non-members in at least one magical skill, and some more than one, so it's still possible to train him up to that level in one skill without ever being able to cast a spell. This can be pretty expensive, though.
Why would a warrior want to join the Mages' Guild, anyhow? Join the Fighter's Guild! See the world!

For recall, water walking, water breathing, and other spells that any character would enjoy! Well, specifically to be able to make a custom spell that is small enough for a big dumb warrior to be able to cast, even with low skill

Bah. We big dumb warrior types seldom remember to how to breathe, anyway. ;p You can get some of those in convenient potion form from a temple or Dark Brotherhood. Sadly, not recall. And potion effects are hard to customize-- it's possible to brew potions that do a lot, but they always get labeled 'Potion of Unknown Effects'. Impossible to sort them out. It's a pain, isn't it?
My three biggie disadvantages when making a character always seem to be no spell points in light, no spell points in darkness, and no regenerating spell points. Pretty much a nega-mage, you can see. There're temples that duplicate potion making, spell making, and item making, the three big advantages of the Mages' Guild. Yeah, I know, none of them offer Teleportation.
If the Aedra had meant us to teleport, they'd have made us with air-mail stamps on our foreheads.

Kidding aside, Jormungandr has a point-- while there are temples that offer single services like in the Mages' Guild, none of them offer all the services in the MG. If you want to be able to do it all, it's the only game in town. It's really just a matter of deciding what you want to do with your character in the long run.