I don't think so. An organization so big and bureaucratic that needs 3 months to authorize a server purchase will for sure need a few weeks of paperwork to authorize a new AWS account creation, and will track the spending for OU and will cut budget and usage if they think you deserve it.

If anyone's curious about the ballpark cost, a carrier-owned (?) DC near me that publishes prices (most don't) advertises a full rack for 650€ per month, including internet @ 20TB/month @ 1 Gbps, and 1kW power.

Though both of which are probably less than you'd need if you needed a full of rack of space, which I assume is part of the reason that pricing is almost always "contact us". I did not bother getting a quote just for the purpose of this comment. But another thing that people need to be less afraid of, when they're looking to actually spend a few digits of money and not just comment about it, is asking for quotes.