Hi Gabe Gabielsen here - This is and Excellent Question
Let me throw in my 2 cents on this subject. The short is it depends. I am a local government consultant. I work with cities, counties, townships, boroughs, villages, parishes and school boards all over the country. My specialties are Economic Development, Facility Construction and Organizational Effectiveness. In addition, I am professional associations and trade organizations often invite me to present workshops and seminars at their annual conventions and conferences.
When I receive an unsolicited invitation to Link I immediately scan the person's or organization's bio. If the invitation is from a person or company that sells phone services, investments, real estate, cars, insurance etc. I ignore the invitation - because has nothing to do with my targeted Linked In profile.
If on the other hand it is from someone in a local government unit or a professional association I immediately accept the invitation they sent and them I sent them a short message informing them I accepted their invitation and ask them "Why did you want to link with me". 99% of the time they'll come back saying a colleague forwarded them one of my articles, told them about a program they heard me present or shared with them a copy of my book. Sometimes these unsolicited invitations come from individuals who are looking for potential resources to contact with problems in their organization.
You need to know I rely heavily on all my linked in contacts for information. I have tagged all my links by specific categories: i.e. Mayors, City Council Members, School Boards, County Boards etc. Sometimes I think it is better not actually knowing my Linked In Contact when the information comes in. For example I recently sent a request to all my Linked In "Mayors" and asked if they could forward me a digital photo of their City's Welcome Sign for a presentation I was preparing for an Economic Development program I was scheduled to present. It was amazing how many Mayors responded that their cities did not have a Special Welcome Sign - they just relied on the green information sign the state required.
Because Mayors did not know me personally they expressed their sincere embarrassment in their reply. They went on about how difficult it was to get their city councils to work effectively together - and just agreeing on a sign formant or a dollar amount to spend for a Welcome Sign was typical of what they have to deal with.
Not only do I have an extensive list of local government "links" but I purge my a;; contacts at least once a year - by sending out a short email message asking ... "Its been some time since we last had contact are you still in you local government position? Many times they will tell me they decided not to run or that they lost their last election --- however many want to know if they can still be a link with me as they enjoy the articles and information I have sent out in the past.
I can tell you for a fact that I have met many wonderful people and gathered extremely valuable information and advice from the individuals who have sent me unsolicited Linked In invitations.
Hope this was of value.