Anyone can respond to a RFP, but realistically they want to know if you have the resources to fulfill whatever it is they want done. Companies that these agencies have already worked with will have an advantage, and frequently they're written so that only one supplier will have the necessary resources but it gives the appearance of open bidding.
I've worked for companies that responded to RFPs on a regular basis, and frequently there would be 20-30 people involved in writing up the response. We would have to document everything from the physical security of our data center to our software development processes, the type of data encryption we used, what our disaster recovery plan looked like, what type of training, certification, degrees the individual members of the staff had, protecting the buyer from lawsuits/licensing issues, and on and on and on...
Consider that the worst thing that might happen is that your RFP is accepted. Then you may have to go through several rounds of meetings with the customer, have your credit and background checked, have audits done, and then you might get the contract. Then you just have to deliver and support the product. And then wait 90 days for payment.
On the other hand people have bluffed their way through.