No, the iPhone SE does not come with 32GB or 128GB of storage.
There are two storage tiers offered with the iPhone SE, 16GB and 64GB.Only the iPhone 6s and iPhone 6s Plus are currently offered with 128GB of storage. Apple typically launches new iPhone models with larger storage capacities, then reduces pricing and storage offerings as they are replaced by updated hardware. For example, the iPhone 6 is still available, however the 128GB iPhone 6 model is no longer manufactured.
Apple does not offer a 32GB storage capacity in its iPhone lineup at this time.