Doesn't always work.
You can pick up your clearance but be held for release.
Happened to me this weekend at when trying to depart KMWO (Middletown OH).
We received our clearance prior to startup, were told to call back for
release when ready to depart, and taxied to the departure end of the
runway. We called back for release from Rwy 05 and were advised that
there was an aircraft ten miles out on the approach to Rwy 23 to the
airport. Winds were 060 at 7kts. After the inbound aircraft went missed,
we called for release and were advised that there was a second aircraft
now inbound on the 23 approach.
We could have requested a VFR departure and gotten out immediately, but
instead elected to wait for the first aircraft to arrive. Little did we
know ATC would slip another aircraft inbound while we waited. The worst
part of this was there was a VFR aircraft behind us who had to wait
because there was not enough room on the taxiway to go around us.

RAM wrote:
As a aside, why pick up your clearance with the hobbs running? Given that
you may not get your filed route and thus may need to study the charts
and/or program the new fight plan into the GPS, pick up your clearance while
still on the ramp and with the engine off. That gives you time to clear
your mind, do last minute tasks and be prepared for flight before starting
to siphon your wallet. I preflight the plane and then pick up the clearance
on my hand-held. Once the route is confirmed, I pick up the highlighter and
start marking the charts. When I start the plane, I am ready to fly.