In my experience yes, but the difference can vary greatly as there are lots of variables.
If I were to print an image with a #2 negative on #2 paper and developed it in a cold tone a neutral and warm tone I would see a very slight difference, mostly between the warm and cold.
The big difference is if you want maximum warm tone or maximum cold tone on corresponding paper. Then you can see a real difference.
I usually have a coldtone bath and a warmtone bath and use both if I want neutral.
Also some developers work faster than others and this will have a bearing as well. So I can use a slow warm developer then a fast cold to maximize the blacks....sorta. Again lots of variables and worth experimenting. Also my experience is limited.
If I were to print an image with a #2 negative on #2 paper and developed it in a cold tone a neutral and warm tone I would see a very slight difference, mostly between the warm and cold.
The big difference is if you want maximum warm tone or maximum cold tone on corresponding paper. Then you can see a real difference.
I usually have a coldtone bath and a warmtone bath and use both if I want neutral.
Also some developers work faster than others and this will have a bearing as well. So I can use a slow warm developer then a fast cold to maximize the blacks....sorta. Again lots of variables and worth experimenting. Also my experience is limited.