If you are a Flying Crew Chief, yes. To be a FCC you must be at least a 5 skill level in your specialty, and if you are a specialist (IE Jet Mech) you will be cut trained into at least one other specialty and Crew Chief. If you are a line mech, you will work the line and deploy (if your jets do) or supplement AMOG as necessary.
As for how often the FCC's are gone, it depends on the airframe;
-10- has at least 2 FCCs on EVERY mission that leaves home station
C-17- It depends on the schedule, but it is VERY rare to find an acft in the TACC system without at least one.
C-141- About the same as the C-17 (and they do take FCC's on the weekly Thule run).
-135 Don't know, but I've never seen a -135 FCC in the system.
AWACS- Same as 135
Fighters deploy with MX
, so if they deploy, you will go, otherwise, not normally.
Airlifters don't deploy, but there is a unit known as AMOG (Air Mobility Ops Group) that provides enroute mx support to airlifters at fwd bases.
-10 and KC
-135 do deploy, and we take our mx with us when we do. There are FCC's in my squadron that are gone as much as I am.
Hope this helps.