Make no mistake, this is a publicity stunt and you shouldn't expect Virgin Atlantic to follow through. But SAF is feasible.

Cost: Currently, according to Argus Media, SAF is around $6.69/gal compared to $2.85/gal for jet fuel. Jet fuel accounts for between 15% and 20% of airline operating costs per US BTS reports. So using SAF would increase operating costs by 22-35%. Given that airfare fluctuates around 20% depending on whether or not it's a tuesday, that's actually not bad at all. (Also, I think the airlines could fully absorb that price increase if it weren't for the deadweight of shareholders, stock value manipulation, and executive bonuses.)

Scaling: Despite how hard America tries, there's only so much used fry oil. Biofuel needs farmland, and there isn't enough farmland to serve the automotive sector. Given typical yields, we would need about 373m acres of biofuel farmland, which is every last inch of unused farmable land the US has. But aviation is a different story. According to the EIA, the US uses 8.81 million barrels of gasoline a day, 2.98 mb/d of diesel, but only 1.5mb/d of jet fuel. That's an order of magnitude less fuel, and an order of magnitude less farmland.

Sustainability: This one's trickier. Biofuel doesn't need to be produced using fossil fuels, but usually is. The US's 893m acres of farmland produce only 10.6% of our GHG emissions. I think the biggest concerns would be increased water, pesticide, and herbicide usage. I am also not sure of the impacts on other nations with different geography or agricultural potential. I am not well-equipped to quantify those impacts.