Without any details, it’s difficult to tell for sure. Processing on GPU is of course much faster but the 2GB might be a bottleneck. The problem is less the dataset size – you can always reduce the batch size – but the complexity of your network, i.e., the number of (trainable) parameters.
I would just give it a try. Install PyTorch with GPU support, create and test your network with a small sample dataset on the CPU (any error messages are usually more helpful compared to GPU). If this seems to work, try to move it on the GPU to see if it works and how the performance looks like.
The good thing is that moving the network and the data onto the GPU is very easy with PyTorch, so you don’t loose anything here.