Yes and no.
Don't forget petroleum itself uses petroleum -- especially if you're comparing wood chips to heating oil which itself takes extensive amounts of fossil fuel to refine and transport. So "carbon neutral" or not, it's significantly less to cut, chip, and transport locally then from the Canadian maritimes, Texas, or Venezuela...and THEN the heat isn't from a fossil source but instead repeats in a current cycle.
Natural Gas, especially coming from Pennsylvania, and where it has far less processing and transportation (pipeline) energy needs might be in the same range of carbon emissions as the petroleum needed to obtain wood chips. I'm not sure; it would be closer to it then heating oil though. However, Salisbury is likely not currently served by natural gas -- though a proposed massive expansion of our natural gas network is now being negotiated by the State, Utilities, and Banks (it's roughly a $2.5 Billion project that involves laying 900 miles of new pipes to serve places like this school, with the goal being to switch our heating mix from 30% NG / 60% oil to 50% Gas / 40% oil within the decade...the banks get involved since many consumers would need loans to convert from oil to gas, though their savings should then offset the loan payments).
As for saving money with wood heat, I have no doubts it is cheaper for me to heat with it. SIGNIFICANTLY cheaper. I have some but not excessive toys. Right now I figure my marginal cash and capitalized costs for my heating run about $160/winter. That doesn't include certain things I would have regardless of burning wood (I would own my 12 acres and pickup whether or not I used it for heating). I'll admit that's exceptionally cheap, and in a few years when I have everything the way I want it I'll probably be more like $350/winter. Which is probably less then the minimum delivery for heating oil nowdays.