I think it is a great idea. In fact, I suggest connecting with people by telephone and even try to meet with them to learn about them, their projects and the company in advance even before applying for a job, even before sending them your resume! Think if it as a job shopping strategy.
Start developing relationships from the moment you get a name. 80-90% of all jobs are never advertised. 80-90% of job seekers look for jobs online which is really ironic when you think about it. Social networking tools like LinkedIn can help you find the connections you need but it's up to you after that to build the best network you can. It's that relationship that adds a person to an otherwise impersonal resume, especially if you've come across well over the phone.
As for connecting on social networking sites like LinkedIn, it would all depend on your profile. If it looks great, has positive endorsements and testimonials and is relevant, why not? I know a few people who got jobs after connecting with their potential employer on Linkedin. One of them shared with me that the employer had pretty much made the decision to hire based on the LinkedIn profile and that the interview actually played a very small part in the decision making process.
They say that a person needs to connect with you in some way anywhere from 5-15 times before they will decide to do business with you. Any opportunity that causes a potential employer to think of you and see you in a positive light is worth it.
Be aware though that this is not a universal feeling amongst all employers. Connecting with some in advance could place them in an uncomfortable position. For example, hiring managers in government or other organizations where they must demonstrate impartiality could be problematic if two candidates are equally qualified.
If you are still worried, why not just ask them if it would be alright for you to connect with them on Linkedin? Not only would you yet again have an opportunity to connect with them (preferably by telephone), but you might come across as someone who thinks before they act which will likely be appreciated.
Remember: Interviews don't start when you walk into the interview room, they start from the moment you first contact a potential employer and end after you've started the job.