The amount of energy that you pay for is dwarfed by air conditioning, certainly. But if we're going to talk environmental impact, you have to count all the other inputs, too.
It would certainly start out less economical, but I still wouldn't care to bet about the final outcome if everything is considered. To some extent it would depend on your accounting; "tons of carbon" isn't my personal favorite.
What other inputs? Sunlight and water? Grass is an efficient way of harvesting solar energy. If you're talking about a growth cycle which doesn't involve animal fertilizer inputs, you've got to have a huge external energy source involved to manufacture fertilizer, so that's a pretty big cost of not raising animals on available pastureland.
That, and don't even get me started on methane emissions, which is a handy way to deflect discussions about CO2, but not a great way to actually do anything productive (look up radiative forcing and the relative atmospheric lifetimes of greenhouse gases).
It would certainly start out less economical, but I still wouldn't care to bet about the final outcome if everything is considered. To some extent it would depend on your accounting; "tons of carbon" isn't my personal favorite.