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The application process takes a couple of days to process, and as well as looking at the website, they look at the WHOIS details to check that you are indeed the rightful owner of the site. At that point they will clearly ban you from Adsense forever. It's not worth trying.
Once you have been approved you can indeed paste the code to other sites you own, but at some point Adsense will clear the junk from the system, and if they have any sense they will cease this policy as it's a huge source of abuse.
If Google is not already confirming site ownership through whois etc., then on Tuesday when they get back to work, someone's going to read this and put it on the agenda for their next weekly meeting.
My main site's account has been in my wife's name to use her tax allowance for a couple of years now, and I have my own account for tinkering around on new ideas. I haven't used it for a while. I wanted to re-activate it a couple of weeks back, and emailed adsense support as I couldn't log in on the account I thought I had registered in. Support told me that I couldn't use my adwords account to log in on - use a different email address and sign up again. I did this, and included the new site's address.
A couple of days later support emailed me to say something along the lines of "Oi - you signed up under ...@...co.uk, use that address to sign in on dingbat". In the two days it took them to process the application, there were two WHOIS lookups showing in the log files.
Now, I'm only assuming that the lookup was adsense support - I don't know this for a fact. However, if you were Adsense, wouldn't you perform this simple check?
But I generally agree that if your policy is to 'hit and run' then you are not going to last very long in this business. Underestimating Google's seriousness about keeping its business clean is a fatal mistake.
In the two days it took them to process the application, there were two WHOIS lookups showing in the log files.
I doubt they were from Google, ever heard of spammers? I used to have an open whois registar but got so fed up with spam idiots hassling me by phone, email and letter that i chose to have complete anonymity via domainsbyproxy
It was after this was set up that i joined adsense and the only way they can find out my details under that system is by legal demand that i must answer by lawyer etc.
so obviously, checking by whois is not something that Google adsense do, at least not usually.
On the other hand, if you re-apply for Adsense with a different name and different website and after approval use the adsense code on a site that was banned before then that's very easy for the Adsense team to detect and ban the new account too.
No matter what you do, if your website violates the TOS, sooner or later they are going to detect it and ban you.
I got an Adsense account after waiting for one hour so sometimes it's the content on the site they look up. If it looks pro enough with plenty of keywords they sign you up right away.