YouTube/iFixit Video
Unfortunately, this doesn't look to be the case.
iFixit has already torn down the Apple Watch, only to discover that the S1 chip that powers the watch has soldered connectors, which means it's extremely doubtful you'll be able to upgrade the first-generation Apple Watch at any point.
"Despite rumors (and hopes) of an upgradable product, the difficulty of removing the S1 alone casts serious doubt on the idea of simply swapping out the internals."
Of course, most Apple fans were probably predicting this would happen. The company's products have always been difficult if not impossible to repair, simply because Apple discourages tinkering with its hardware. That said, the rationale for having an upgradable Apple Watch made sense: Most watches last for decades, and they tend to be passed down from generation to generation. Some believed the ability to upgrade a few internals in the Apple Watch would make it so you could pass down a first-generation Apple Watch to your child or grandchild and it would still be functional for them (besides telling the time).
But that's not the case. Apple will instead push customers to buy the newest Apple Watches when they come out, as the first-generation Apple Watch will be frozen in time.