If you mark the job as invite-only ... make sure that what you are sending is an Invite and not an Offer. If you send a direct offer to an invite-only job, the freelancer cant read the job description because its invite-only. Huh!
@ Michael S - smart move to have done your homework in advance. My compliments.
Even on Invite Only jobs I believe that Upwork still gives you the option to add their choice of providers thus defeating your intent. Make sure you do NOT click the button or whatever is used for that purpose.