Can i convert worlds from 1.5.2 to 1.7.2?

So im doing a map in 1.5.2 right now,and im also thinking of buying minecraft,but im not sure if you can convert 1.5.2 worlds to 1.7.2 +,im asking this because from 1.5.2 and 1.6.2 and 1.7.2 changed really much,like the game updates,maybe mod installing,there were added new biomes,and really much new stuff was updated. So i just wanna know if my map will convert with everything saved and without anything deleted or new biomes added. Yes i could save my map and try 1.7.2 but then i'll need to downgrade to 1.5.2 if something doesant work. And the map is also built in World Painter so its a custom one. And another problem is that i heard there is a lack of mods for 1.7.2...but so far i use only TMI (Too Many Items)...so whats your opinion guys?

Anyway,thank you for reading this and helping me