Seeker is a firm is using a talent management portal (be it Taleo, Brassring or whatever else) then ultimately your application will wind up there, regardless of how you approach the firm.
I would usually recommend a dual approach - assuming you have contacts in your target firms. Reaching out to people within the organisation is useful, and for those with a less than impeccable profile can be productive, but is often mishandled (i.e. people put themselves forward as candidates rather than using it as a networking/information gathering exercise with a potential internal referral off the back of that).
Best approach for an advertised role - apply through the route they ask you to use (website, email the internal or whatever it is) and back that up with a note to x contact at the firm, making them aware of your application, asking for any guidance they can give on who you could talk to to add a little weight to your application. Dont ask them to do the work for you (MCs can be political places, and unless they know you very well indeed may be reluctant to out their own name to someone they cannot be absolutely confident will get an offer).
Linkedin is a great tool, but its not really one for applying for jobs through individuals - that is effectively using LI as a sales channel, and that doesnt work well. It is email after all and you cannot sell over email. Use LI as a networking tool to support and inform applications but not the main route.