Yes. Well, not for a long time, but mixed (upto 1:1) with diesel, yes. The diesel is needed (with the Tdi's) to lubricate parts that other oils can't reach. Apparently the early Td5 engine will happily run neat paraffin, but I'm not sure how you tell which pumps are safe.
I've happily burned paraffin/veg oil/diesel/petrol mixes at various proportions. Ran 1:2 paraffin:veg oil for a while in 2008, just because I had a few litres of paraffin from a previous project and had spent all my money on discovery parts. Crudely filtered stale petrol that's been sat around in motorbikes or generators for months doesn't seem to bother it either.
It's most use for thinning other fuels. Can't say I'd trust the purity of garden centre paraffin in an engine with a lambda sensor though.