Sticky question!!! You can develop a city without using diamonds. You can even develop a pretty nice city without diamonds. Some of the original Elvenar players didn't use diamonds, and are in the top 100 of their worlds.
From there, we have a difference of opinions. I have a city on Winyandor, if you want to use it as reference, all built without purchases, except for 1 builder. But the builder wasn't necessary, just convenient.
That city is at a stage where the no-pay model is beginning to hit what some of us consider a roadblock, others just consider a requirement to play differently. There's a new limit to the number of grid expansions players can earn, so it can be like driving along and suddenly shifting into 1st gear. In Elvenar, getting expansions is pretty crucial, since there's always the want to build or upgrade. For no-pay, there comes that point where you have to play for several months with very few expansions.
My opinion - Elvenar for no-pay can be fun if you're patient and it's not your primary entertainment. It's kind of the thing you do when you have a few minutes here and there, except for some serious time rearranging of your city periodically. If you let yourself feel pressured to go big or fast, you'll likely feel frustrated as a no pay. Heck, even moderate pay players are feeling some frustration since being slowed down.
You also might want to look at your boosted goods, then look at players further along to see how your buildings look - whether it interests you or not. Upgrading is a lot of the reward in Elvenar, so you'll want to have buildings you really like. If you don't like the look, by all means join another world and see if you luck into something you like more!
Good luck! There's a link for a Player's Guide here in the forum that explains much more than this. Ciao.