For quick question a quick answer:
If this script is running under same circumstances on clients and
on server, and variables being changed upon global events, it
will be.
Now the not so quick answer:
This really depends on how you setup your script/execution.
If you declare a global variable on a script, which is only locally
executing - no other network-participiant will ever even know
about existance of this variable.
You should predefine such variables in some init script (init.sqs),
and when changing it's state/value - use publicVariable command.
Oh and there's much more to tell about this, but it's already all been written here on these boards, and i'm too lazy now to get into
detail another one more time.
Best is you take some time and read through some threads in
multiplayer editing/scripting - that way you do not even only read
about how things has to be done - the more you'll read also about
problems and their solutions
~S~ CD