This isn't particularly a Project question per se. However, given the
generality of the question "is it possible for resources to be notified
by SMS when tasks are assigned to them", the answer is "Yes it is possible".
Any additional detail depends on exactly what it is you want to achieve,
why and what your Project set up is.
The solution could be as crude as you typing the assignment directly
into an application which then sends it by SMS. The othe end of the
spectrum is a highly integrated system in which your organisation's IT
systems forward emails to a mobile handset for example (over the SMS
infrastructure).
So the solution you end up with depends partly on how much work you or
your organisation is prepared to do.
The other point I would raise is exactly what is the problem you are
trying to solve because the desire to use SMS actually sounds like a
solution rather than a statement of the problem? Why do you want to use
specifically SMS when handsets these days are capable as acting as
extensions to your organisation's LAN and supporting the normal set of
applications such as email clients and web browsers?
Dave