I started out as a handler for Fedex, worked there for about 7 years and eventually getting a ramp agent gig. Back then, they were known to hire with no experience into GOC if you had a license. So, I went to get my license and FDX was nice enough to pay for it (tuition reimbursement). That was June 2001. We all know what happened in September and that pretty mnuch stopped their plans for hiring/expansion for while. I did get a dispatcher gig with a local supplemental and worked both for a few months before I threw in the towel at FDX. When I left they were only hiring internal to the Air Ops department.
We did have several guys from my ramp crew get in at GOC, but all were current Valujet dispatchers... and most left Fedex for Delta a couple years later.
UPS is a different beast. While in the past they have hired line dispatchers from within the company who had no experience, that hasn't happened in 8 years, and before her it had been years. So since then it's been all external hires with minimum of 3-5 years experience... usually international heavy experience. In the last 10 years (can't speak to prior... pre union it was all different), there's not been any kind of "internal only" postings like FDX would do. If you worked for UPS box throwing and met the hiring requirements, you went through the same process as an external hire.
On the other hand, if you are are interested in a supervisor position and have no experience, they will hire you into that. There's no movement from the line dispatchers into management... for a reason... and they have to fill them some how.
As far as experience. At some point you have to be hired without experience, might as well be a major right? But not the way it happens for most. SO experience can be very helpful in a career, but we have some of our more experienced dispatchers who... well frankly it's like it's their first day every day. Experience in other areas that require good time management skills, attention to detail, and critical thinking in pressure situations should be a consideration. But that's hard to measure and post for.