Any edge that the rats can get their teeth around, they are likely to chew. Although fixing the front of the drawer is a relatively easy fix with some hardware cloth, what about the other sides?
When the unit is closed, what do the sides and back look like inside that outer shell? I've seen similar units that the rodents wouldn't even have to chew out of, they could just jump out of the drawer. Something that is designed to hold clothes or similar items is not likely to have all the drawers sealed enough to keep rodents in.
Although it is possible this will work, I'm afraid it is very likely that it won't, and then you'll have a disaster with loose rats everywhere. Even if it appears to work for a while, you might eventually get a rat that is more prone to chewing, or a day when they are hungry because you didn't put in quite enough food, or it might gradually warp & sag over time. I'm sure you'd be happier in the long run if you built a proper rack. If the lack of tools really makes that impossible, you could make tubs like the ones in this thread:
http://www.ball-pythons.net/forums/s...ad.php?t=56321
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