Hi,
Yes, that is possible. It is called routed access design, meaning you are routing at the access layer switches. The draw back of that design is since the vlans are local to each each switch, you can't span a vlan across multiple switches/closets which can be a problem if you need to have 2 user on 2 different switches or closets that need to be in the same vlan. Most common practice is not to route at the access, but rather on the distribution layer. If you have a collapsed distro/core layer, then you route at the core layer.
HTH