Well actually, your original assertion is that the guest worker program would double the current level of demand—we have 10 million now and you envisioned 10 million more. There just isn't anything inherent in the guest-worker plan that will do that. So the question shouldn't be whether this will make things worse but whether this will make things better.
Wage statistics on illegal immigrants are obviously hard to come by, but the estimates I've seen say that at least a third of illegals actually present papers (e.g. fake/stolen SSNs) such that the employer can at least claim not to know he's hiring an illegal. In those cases the illegal is certainly receiving minimum wage or above. Where the employer is paying less than minimum wage, we can classify that as criminal intent, and filtering out the (let's suppose) one-third of "honest" illegal hirers will still make it easier to crack down on the rest.
Also, consider that the risk of prosecution represents a cost to the employer. The employee's effective wage is thus the real wage plus this "risk tax." Presumably the effective wage the employer is willing to pay stays constant. Therefore, by eliminating the risk tax for an employer, we allow him to pay the employee more. In some cases, this will mean that an employer willing to pay an illegal below minimum wage will be willing to pay a guest worker at or above minimum wage.
So yes, it is probably unrealistic to think that 100% of the current demand for illegal immigrants will be sastified by the guest worker program. It's even possible that the sum of guest workers plus the reduced number of illegal immigrants will be higher than the current number of illegal immigrants. The number of illegals will not rise, however, and every guest worker hired is one new job added to our economy.
Yes, an exaggeration...I agree, to say that the number will double. But I stick to the assertion that the guest worker program will not change the current level of demand for illegal workers. I hope I am wrong about that and you are right! Only time will tell. I do not believe that demand for the illegals will just dry up because of this. There will still be individuals and companies willing to take the chance. The net effect could in fact be positive though as you pointed out. Something has to be done...