Gentrification is a complex and specific topic. I think you're asking whether Belltown is pricey, upscale, etc. I'm going to answer both ways though:
Belltown was never really a economically depressed, low-income area. It is right in downtown Seattle and has luxury, high-rise condo buildings that were built in the 1980s (so it's been a place for luxury living for at least 30+ years). There are areas of Seattle in which gentrification is in full-swing and is causing property prices to rise dramatically and is displacing long-term residents--Central District, First Hill, Columbia City, and other neighborhoods
From at least the early 1980s to now, Belltown continues to be a popular area for residential living and has seen a number of new, architecturally-cool buildings go up in recent years. There are no houses in Belltown--it's all condo living. A person that lived in Belltown could walk to work just about anywhere in downtown or South Lake Union. They could actually shop on foot for some seafood at the famous Pike Place Market and could walk a few blocks from home to catch a Broadway-quality show. It is truly urban living and the prices reflect that. In a recent rental survey, Belltown was one of the most expensive neighborhoods in Seattle with a one br median rent of $2,595.
What kind of people live there? inside the buildings, people who can afford that kind of housing payment. In terms of age & other demographics, it is perhaps a much more diverse neighborhood than many in Seattle; old and young, many different backgrounds. Outside of the buildings are quite a few homeless people or transients. If you want city living, with all it's pros and cons, Belltown is the place to be.