The "three PCs" allowance is only for the Home and Student edition. For most
of the other editions, the rule is one desktop and one laptop.
Read the End User License Agreement to find out what's valid for the edition
you have. Most easily, go to Office button > Word Options > Resources, click
the About button, and click the blue link for View the Microsoft Software
License Terms. Look for the section titled Installation and Use Rights, and
specifically for the subsection labeled Portable Device (an interesting
description of a laptop).
The short answer is "probably yes, but make sure".