Do you mean if you install it on your desktop, will it work on your portable device, like tablet or phone? or on a different OS, like mac?
for the tablet or phone, I do not believe that extensions are enabled on the mobile versions of chrome. Some extensions need the desktop environment to work properly, and mobile platforms simply do not have that.
As for a different OS, I believe that chrome for mac has extensions enabled, and they should work the same on Macs as well as PCs.
this isnt to say that mobile chrome will never have extensions, it just simply hasn't been implemented yet