This article is from the FAQ, by with numerous contributions by others.
Theoretically, Yes. The INS often presumes that the alien entered the
U.S. in another category with a preconceived intent to attend school and
circumvent the normal visa issuing process. This is particularly true if
the change is requested shortly after entering the U.S. A wait of 60 to
90 days before switching is advisable in order to avoid presumptions of
fraud. As a practical matter, unless there are any indications of fraud,
change of status to F-1 is relatively a simple matter.