Yes, but now you know that you put the carbon inside the tent and draw through it, use a passive intake to vent the tent, and then use a 2nd fan to cool the hoods by either pulling or pushing air from outside the tent to the hoods to outside the tent. That was your original question!!! We all agree on that.
To sum up gnome and mine's argument, he says that a fan is drastically more efficient pulling air and I say the difference is fairly minimal. I say that your hood ducting has a good chance of leaking air, and gnome says that the chance is very slight. Certainly the length and design of your ducting and hood as well as the power of your fan will all come into play. It won't be tough to try it both ways! Try pushing if you want the best from a security standpoint and if you can't get the hood cool to the touch, just pop the fan off and flip it. Pretty simple really. you should be able to put your hand on the hoods and not burn yourself. Cool to the touch is ideal.
Here is a link to the information about the reflective materials. For a tent mylar is probably not optimal because it is only really effective when installed smoothly according to the guy who wrote this faq. You may want to use something to block IR outside of the tent however, if you can't use it inside. Depending on where you live and where in your house the tent is located it may not even be necessary. The IR camera tapes I have seen all show the IR coming from either the box sill (the piece of wood that sits on top of the foundation and attaches to the floor joists) which in dicates a basement grow op, or through the roof which indicates attics. just research all of that before you decide what to do. Most grow ops are busted because the farmer tells people he is growing, or neighbors smell it. IR detection isn't the usual reason. Many communities don't ever even do that, and the feds aren't scouring the entire country.
Jed