Sorry, the VCCR makes no distinction regarding legal vs. illegal immigration. That's to keep the host government from simply revoking a visa and saying "he's here illegally, so he's no longer under the Vienna Convention."
Again, do really think we contact their government every time we send one back?
We send a summary report saying "So-and-so detained on 5/5/06, deported on 5/8/06." That's the sole requirement for immigration-related offenses.
When we detain and hold them on a felony charge, that's when the requirement to allow consular visits comes into play.
Remember that EP-3E that got smacked by a ChiCom MiG 5 years ago? Technically, the crew didn't legally enter China, and the ChiComs were making noises about charging them with murder. By your standard, the ChiComs could've said "screw you, pal" to requests for consular visits, and we'd've never seen them again--and we'd have exactly zero argument.
If that's what you want for Americans, say so plainly. Just remember that whatever rules you seek to impose on foreigners will be imposed on your fellow Americans.
That E3-3E was given permission to land on Chinese soil.
I know--but that's not the issue here. I'm talking about your garden variety illegal invader here. Not the ones who have committed felonies. I hope we can catch them and send them back before they have a chance to commit a felony. So yes, do the VCCR dance once we imprison one if you must but send the others back as soon as possible with a note from their captor showing date caught, released and a bill from the American taxpayers.