You would probably be pleasantly surprised to know that a lot of decent companies will offer you lunch on your first day, or some other means to compensate and welcome you. If not your employer, then one or multiple of your coworkers. Other means of compensation will certainly present themselves.
As for entitlement to compensation, the answer to your question is no unless you have it in your job offer that they will compensate you for any fees that you have to incur in order to finalize your employment. I've had that before, in the form of transportation vouchers. Any form of compensation will certainly be a nice gesture.
As for whether or not it counts as work, the answer to your question is maybe - under §785.11 of the Fair Labor Standards Act, as the FLSA counts anything "suffered or permitted" to work as payable, as long as it reaches certain criteria. If they made it clear that you can do it when you get there, then the answer is no, as a criterion is that it must be mandatory and outside of work hours. Otherwise, then maybe. But I'd advise against it as it's minimal and rocks the boat.
On another note, in the future, might I suggest free services, or at least free trials of services, that offer signatures? I use SmallPDF and PDFEscape, which allow you to insert text and draw signatures. If a company requires a fax then I find a fax service online where I upload the document and it's faxed for me. I've found free services, but the last service I used was a dollar. If the forms are not sent to me digitally, then I simply go get a copy of those forms online since the IRS offers them anyway.