No.

Static variables will be available across the whole app domain.  It is
conceivable that two clients hitting the same page at the same time would
have two threads trying to modify that variable at the same time.

You will need to add some synchronising code such as:-

static SomeType ourValue = null;
static readonly object ourLock = new object();

public static void ValueMutator()
{
   lock(ourLock);
   {
       // code that modified ourValue;
   }
}

Of course the exact nature of the locking needed (if any) will depend on the
page logic.