The answer is no. You can view your RJOBRIEN account on their website and see your positions. You can view Equities Positions on TradeStation Website. Unfortunately there is no execution ability on either site. I agree kinda lame. You need to download the platform to another computer.
I personally travel with my Laptop with TS on it.
All I need is a Wi-Fi or dial up location.
You can always call their trading desk to get executed in a pinch for an extra $20. Good Luck.
ebo