when I first started doing it back in 2017 or so it took one or two days
at some point (maybe 2019? I don't remember) things seemed to have been changed and from then on transfers have been immediate (as in, less than the time it takes for me to log in to my CX account) for me
keep in mind that I haven't actually made a transfer to CX since 2020, though
if the concern is specifically about award availability disappearing, I seem to remember CX being willing to hold award tickets for a while when calling - dunno if this is specifically a status benefit