Maybe a stoopid question, but...
 

...when you drop out a rear wheel (say to fit the bike into a car), does the chain have to be replaced in the same cog positions to match what reads on the handlebar shifter numbers, when re-fitting the wheel?

Easiest method for R wheel removal and install is to shift chain down to smallest cog. Makes it easier to get the chain back on the cassette when putting wheel back.

^ This. Make it a habit to shift into smallest cog before removing the wheel, and the re-install is a snap. Do this for flat tires, too.

Thank you both - I guess I'll shift both levers to number 1 then, and pull the chain onto the appropriate cog.

No. Shift the rear shifter to the smallest cog. Most rear shifters have number 1 as the largest cog not the smallest. You don't have to touch the front shifter

Thank you.

But to answer your actual question - no it doesn't, and it isn't a stupid question.

If you don't shift down to the smallest sprocket, but are somewhere in the middle, It's best if you put it back on the sprocket it was on when you took the wheel off, but approximately is fine. The approximately will be obvious by where the chain wants to go when you're putting the wheel on, because of the derailleur position. It will probably just go onto the correct sprocket. But if not, it will probably be close, and the chain will shift to the derailleur position as soon as the rear wheel starts turning.

Yeah, but sometimes as you are trying to align things you can put it on a cog that is too far away from where the derailleur is positioned. This can result in difficulty in getting the wheel in the frame at a minimum and bend things if you try to force it. Best practice is noted above: shift to the smallest cog before removing the wheel or with the wheel out of the frame before you re-install. No guessing required and the easiest installation.

Oh, yeah, I agree with putting it on the smallest cog. I was just trying to answer his question. I intend to put it on the smallest cog, but sometimes forget. It's not a big deal at all, just not optimal.

No, you don’t have to. It may be easier to shift into the highest gear but sometimes you forget. Just put the wheel into place on a convenient gear close to where it was when you took the wheel out. Lift the rear of the bike and spin the wheel around to get the chain onto the proper gear.