It depends what you mean by "cut tiles." Certainly an angle grinder has sufficient power to turn a disc of abrasive material and force it into a ceramic or concerete tile. But it will probably perform very poorly compared to a wet saw for two reasons:
1) It's not guided in any way. A tile saw is set up like a table saw, you push the tile into a diamond-edged blade. Because tiles are very brittle, it would be extremely difficult to cut one with any kind of precision (and without breaking it) using a handheld tool. It's probably also quite dangerous.
2) It's not cooled. A wet saw uses water to keep the blade cool. The consequences of this are that the "blade" or abrasive disc on the grinder would wear very quickly when cutting an extremely hard substance such as a ceramic tile.
If your needs are really basic, then I'd just get a manual tile cutter for straight cuts and/or a tile nipper for anything else.
On the other hand a cheap tile saw is actually really cheap. Cheaper than an angle grinder, and far cheaper than an angle grinder + a diamond blade. I think this is one of those situations where it makes a lot of sense to use the right tool.
I've done a lot of tiling with low-end tile saws. They really work fine for light-duty work. I'm sure it wouldn't hold up well in heavy-duty use, but for the occasional tiling job, they work fine.