No, sorry there are no ties. And, if you want to separately purchase the second place logo, no arrangement is to be made with that designer (for that logo and/or other work) until after you declare a winner in the contest and (I believe) until you approve final files of the winner. This is because other work or deals cannot be taken into account or influence you when deciding who will win the contest, since the winner not only gets the only prize money, they also get more points toward site ranking/placement than second and third, etc.).
(Also, if you do offer to buy the second place, it is completely up to the designer whether they will take your offer. You would need to make payment arrangements, file transfer, etc. directly with them, since it would not be going through logo tournament at that point.)
I don't know how well I have described the process, I think i have described the in's and out's correctly, but staff could probably clarify this more if you need more info.