Is it OK to drill through a jack stud/full stud pair to cut a hole for water heater drain pipe?
There are general guidelines for dealing with cuts in wood framing.  For load bearing the basics are that you can notch 25% of the stud or 40% diameter for a hole.  


Note: Notches should not be square - this provides a weak point in the stud.  Half circle your notches if you can.

Now there are ways around this if you need a bigger notch or hole.  In my area local inspectors will let you double up the studs and go 35%S and 60% respectively on load bearing walls.  This doubling up is a one time allowance - I couldn't do a whole wall like that.

For electricity these guidelines are more than enough to run several lines through a wall.  For plumbing though you might need to use different width boards (frame wall with 2x6) or use structural bracing.



Note that in the picture you see both wall plates (which offer little structural support) and bracing around the plumbing cut-outs.  When you buy bracing for plumbing there will be guidelines on the use of the product.  Follow those to figure out hole and notch sizing.

For this instance:  If I read right you need a pipe to run perpendicular to the studs.  The same rule applies.  I we are talking 2x4 construction that means that you have 1.5 inches going across.  Mean you can notch 3/8" which isn't much.  There are several ways to handle this is you have a larger pipe (a heater shouldn't need much though) needing out.  


You could notch a little out of each jack and king.  Would be enough for a 1/2 inch pipe and I would feel perfectly fine about a half inch hole with a jack and king supporting each other.
You could rip the king out.  Flip the king stud around sideways and install 2 kings and bore a hole through the center of it.  If you needed a bigger hole you can use 2x6.
Buy a structural brace/shoe.  With a properly installed shoe you can cut out the whole stud and have a ton of space to run things.  Downside is they are expensive (relatively) and getting what you want isn't always easy.


I am sure there are other options but I would need to see a picture.  I would also add if you want to get it passed by local municipality then I would just ask your inspector what he/she wants.