No, definitely not!
The HeatPal burns across a hole that is 3-4 inches. Paraffin will burn in it fine I'm sure, but the resulting soot and fumes would be atrocious, not to mention unsafe. There might be a risk of explosion or severe flare-up.
If I had a burner to spare it might be an interesting experiment, but I'm pretty sure the results would be catastrophic for the unit!
The instructions with it are quite clear - only alcohol.
I would like to know what one of these are and where to get one. I'm intrigued.
Yes, definitely only alcohol.
On another safety note, on the several Websites that I've seen this stove I haven't seen much mention of the dangers of carbon monoxide.
Good ventilation is literally vital if you use this kind of heater.