Very true. I think on the balance of everything I'd just be upfront about it, and head it off by saying "I do hope that if this process goes well, that it isn't going to affect my negotiating position when if/ when the time comes".
As an MD of a recruitment company, my advice would be that you have two options: Come clean and give them the full facts, or commit to the lie but be prepared to get caught out. Coming clean definitely lowers your negotiation power a bit, but it shows you are trustworthy. Depending on the...