I assume you would because the boggart had the same affects on Harry as the real dementors did. I am sure the boggart wouldnt take form of the basilik because no one alive actually knows what it looks like so they wouldn't be afraid of it.
Ginny Mallya edit-No, although it had dementor like qualities, I the boggart-dementor cannot suck out your soul. Same way a boggart-basilisk will not pertify or kill you. But if you are really unsure, ask J.K. Rowling!!! ;P
Elektra Procyon edit : In Harry Potter and the Prisoner of Azkaban, Remus Lupin gives Harry private lessons on how to defeat Dementors, using a Boggart as a replacement. However, when Harry faced the Boggart the first and second time, when he failed to beat it, the Boggart/Dementor had managed to make Harry hear his mother's screams. This may imply that Boggarts can gain some abilities of the thing it morphs into. It also gained its weakness as it could be defeated by Harry's Patronus.. But i agree with Ginny Mallya that if the boggart is a basilisk ,it won't petrefy you.( Remus Lupin's boggart turned in a full moon but he didn't get transformed in a werewolf).
As a side note, some people know what a basilisk looks like, as youre only in danger of death if you look DIRECTLY into its eyes. Advert your eyes from its, and you can look at the rest of its body just fine. Also, because Tom Riddle was never petrified or killed by the basilisk when he first opened the chamber of secrets, it can be assumed that death does not happen automatically, and a basilisk has some control over its ability to kill with a glare. Slytherin's basilisk, then, would not kill the heir of slytherin.