I would certainly expect it to be faster than procurement, but not living in the US the concept of receiving a Cheque in the 21st century would raise all forms of red flags. If they deposited the cash directly into my account via a BACS payment, same as my salary, that would be far more believable.
That said, $10k in office expenses for someone starting on $40k a year ($20/hr training) would also raise a flag.
Edit: Do people really get paid by checks in the US?