It would be better to find a 6amp transformer if you can, the supply regulation will be a lot better.
However if you are determined to go down this route, yes it will work if the transformers are identical, you have to beware of one transformer supplying more current than the other two and overheating.
Also, instead of using three 2200uf caps, you could use one 6800uF (?) cap if it is available.
Woahhh... I just re-read your post.
You are making three power supplies and connecting to 0v (-ve) side to a common point and using three separate +ve supplies. Yes that is no problem.
I had started to think you were making three power supplies to connect in parallel. This can work OK, but it is better not to.
JimB