Alex automatically turned when grabbed. Alex did not fear much and something that cannot be killed is not one of his fears. The idea of leaving made him feel weak. Pride aside it would probably be best to run. Not for his sake but because Elsa wanted him to. 
"... Lets go than... But how will we leave without being seen?" Alex asks.
The smoke in the air began to lessen. Things could be seen more clearly and breathing would be slightly easier. Also it would be easier to be seen. Alex still wanted to kill the beast. Killing it will be an even greater feat when it is unable to be killed. But he would put her wishes before his. That's too bad, only little minions were slain today.
Alex was hunk in of multiple things. The childish idea or even a joke of trying to dig downward and leave underground came to mind. Suicide, Running, Teleporting, and etc. Most of which were out of reach way to get out of there. He would leave he decision up to Elsa trusting her judgement. But attempting to run seemed best to him.