Quick technical thing, unless someone has been in prison, they don't get deported, they get 'administratively removed', so he will have a removal order against him.
Also expatin, you can be illegal and get married to an eu citizen in the uk, you just have to apply for a coa first, which the government have to grant them because its against their human rights not to, but just because they are allowed to get married doesnt mean the UKBA won't remove them before they are able to (they have the right to get married, but not the right to be in the country).
If he's not got much money to his name, he'd have to find an awfully well off woman to marry, or he has no chance. It would be legally incredibly expensive to change from being an illegal to legal via marriage in country because you'd have to have an awfully good solicitor, and even with genuine marriages the chances are only 50/50. Most likely he would have to leave back to his home country and apply there, and if he was caught to have done a sham marriage, then he'd face an automatic ban to the UK of 10 years, even if he tried to re-enter on a settlement visa. So basically, this guy has very little chance.
He's not on the run if he's signing on with the HO, they will just be waiting to get his travel documentation in order to remove him.