No. Wheelchairs are a tool for mobility. High C-level injuries usually require that the individual use a power wheelchair. Low C-level injuries and below usually allow the person to use a manual chair. Advantages of manual chairs are that they cost less, weigh less, disassemble into smaller pieces and are more agile. However, for the person who needs a powerchair, the independence afforded by them is worth the limitations. Some people are able to use braces and crutches for ambulation. These methods of mobility do not mean that the person will never use a wheelchair. Many people who use braces still find wheelchairs more useful for longer distances. However, the therapeutic and activity levels allowed by standing or walking briefly may make braces a reasonable alternative for some people.
Of course, people who use wheelchairs aren't always in them. They drive, swim, fly planes, ski, and do many activities out of their chair. If you hang around people who use wheelchairs long enough, you may see them sitting in the grass pulling weeds, sitting on your couch, or playing on the floor with children or pets. And of course, people who use wheelchairs don't sleep in them, they sleep in a bed. No one is "wheelchair bound."