I would say: pick up the phone and call them! You may want to discuss other things than file format. I'm thinking of for instance how much bleed you'll have to provide.
Chances are that they will accept .Ai files. Make sure you use CMYK colours, though.
The OP's InDesign Policies are probably the best way to go to link the image and prepare it at twice the resolution they expect for out put since they are printing at 200%.
However in the past many AI user would mark the Illustrator option to include linked images as a precaution. And then outline the fonts as well.
And then some made a pdf of that file as well.
I usually do not print from AI but when I have I have sent both the AI file and PDF as well and packaged the fonts and images. I have never outlined the fonts.
I agree with stevenwh504, contact the print provider. That is an over-sized offset print job which leads me to believe it is going to be printed on a large format inkjet printer. If that's the case, you can prep the entire file at 100% ( no need to scale ). Even if you could find an offset web printer, the file can still be supplied at 100%. But, as Zimmerman has suggested, the file's resolution would need to be supplied to the end output device's specifications, which you will get from the print provider. The vendor will tell you what they need. It could come down to a press quality PDF, an EPS, or a live .ai file. The vendor can also tell you what size to make the file and if they need certain things like trim marks, OP's ( over prints ) and bleeds.
From my experience working for printers:
- if it is just one off then most likely it will be printed using digital machine so you can and even should leave your photo/image as RGB,
- leave at least 3mm bleed all around, most printers would need at least that,
- convert all fonts to outlines - sending fonts is actually illegal unless they are common fonts you got with Adobe software or operating system,
- leave file as .ai - I have never heard about printing company that wouldn't have Illustrator, although may be worth to check version they can accept
- on the .pdf I would say it is not necessary as it does require some knowledge i.e. do not use comprssion, setup bleed etc, so I would stick with .ai
I'd say it's safer to contact the company so you can make sure that you were able to communicate to them what you want to print and how you want it printed. And they tell what you will need to give them (i.e. file formats, supplementary files, etc.)
You may want to talk about supplementary things than file format. I'm thoughts of for example how a great deal bleeds you'll have to provide. Probability is that they will agree to. All file and PDF as fine and package the fonts and metaphors. I have not at all outlined the fonts.