No they aren't. I'm pretty sure their relationship in X-Men Evolution is similar to other versions of the X-Men.
Storm grew up in Morocco, where her parents were killed in a earth quake. She was then forced to steal things in order to survive. Professor Xavier saved her from that life and took her in. That's why they are close. Of course she'd be upset if she thought Charles was dead.
No, it's plus of like if Logan were to go missing and Rogue would freak out. A father-daughter type of relationship. I'm sure Jean and Cyclops would go crazy ou really really depressed if Xavier went missing too (look what happened to scott in WATX. yes part of that was jean, but he would have gone just as crazy otherwise). They both are like children to him, being his first two students and all. Storm is just one he was able to successfully reform...wonder if that successful reform will ever completely push itself on Gambit? Any who, they are NOT a couple.
Besides, in the comics the Professor was married to Amelia Voght, heartbroken over Moira MacTaggert, and secretly crushing on Jean Grey so Storm has nothing to worry about.