Probably not. But especially in emergencies it's often better to ask for forgiveness than to ask for permission. (Also, domestic in-state political signaling.)

Anyhow, the legal effect may be irrelevant if the gas producers wouldn't bother trying to export. I would imagine that producers are having trouble just delivering on their long-term, fixed-price contracts in Texas. The short-term prices might be so jacked up precisely because there's little to no surplus to export, period.