Aside from the fact that your attic can be very dirty, you need to be concerned about the following:

• If you have any gas heating equipment in the attic (central heat, water heater(s)), they may not meet regulations to allow them to be connected to the house's main air supply. You can run a major carbon monoxide (CO) risk from improper ventilation of gas-burning equipment.
• Pest control companies can use harsher "dusting" pesticides in attic spaces - stuff you really don't want joining you in the house. Insulation is often loose and can irritating. If you have a much older house that might have asbestos insulation, then you have other problems as well.
• When you pull air out of the attic, it's repopulated by the air from outside. If the air outside is very cold, your attic could reach new low temperatures, freezing pipes or causing other damage. (This may or may not happen, but it's something I would make sure of before attempting this.)

This could be an option, as long as a few conditions are met.

There should be a damper

A damper will prevent outside air from entering the exhaust pipe, traveling down the length and entering the conditioned space. Most exhaust vent covers are designed in such a way, so that even on windy days the exhaust can still be exhausted. If you just have a pipe pointing to the outside, it's possible the outside air pressure can overcome the exhaust air pressure preventing the exhaust from exhausting.

There shouldn't be a way for the exhaust to reenter the building

If you simply close the window on a pipe that does not completely fill the opening, it's very likely that air pressure differences will force the exhausted air right back in the window. You'll want to devise a way to prevent the exhausted air from reentering the building. This other answer illustrates a way to install the vent, while blocking the entire window opening.