By 1864, there were recruit depots at Monticello and Washington. I haven't seen any records of any other depots still functioning by this time, but some other contributors may have better information on this.

Regarding any possible records -- after the Spring of 1864 there are almost no regimental muster rolls, or personnel records of any kind. So it's pretty unlikely that a conscript who died before being mustered into service would have any records. If you'll email me the man's name, I'll see if there is any sort of hospital record or something like that.