I certainly would. IF a layer of hard packed snow/ice, then I might have it on for a short while.
But it depends on what kind of a job you are happy with.
/ Should I take the tooth Bar off my FEL to remove snow?
Yes - unless you are in an area with certain melting after storms, in which case you could probably get by leaving an inch or two behind by tilting bucket to not dig in and let the rest melt. In sustained winter conditions you want to be able to scrape the packed snow-ice down with the edge of the bucket and that would be nearly impossible to do without driveway damage with teeth on.
/ Should I take the tooth Bar off my FEL to remove snow?