Your bike is a lot tougher than you think. I would never give it a moment of thought to put it on the rack if that's what you need to do. The effect on your mileage will be miniscule on the grand scheme of things. Really, if it costs you an extra $5.00 in gasoline, so what? I have hauled multiple bikes on a cheap $60 Allen rack on long distance trips of up to 900 miles one way. Never a problem. Last summer I took a brand new bike on the rack 800 miles one way, and it poured down rain the entire trip. I wasn't happy about it, but the car was too full to carry the bike inside.

I would suggest however that you run a bungy cord from the rack, through the front wheel, frame, and rear wheel, and back to the rack to prevent wheels spinning, and vibrating loose.

I'd spend more time riding my bike and less time thinking about it.