Sometimes. Symptoms of hypoglycemia are divided into the adrenergic and the
neuroglycopenic.  Adrenergic responses are caused by increased activity of
the autonomic nervous system and may be triggered by a rapid fall in blood
glucose (bG) or by low absolute bG levels; symptoms include

   weakness
   sweating
   tachycardia
   palpitations
   tremor
   nervousness
   irritability (sound familiar?)
   tingling of mouth and fingers
   hunger
   nausea or vomiting (unusual)

The autonomic nervous system activity also causes the secretion of epinephrine,
glucagon, cortisol and growth hormone.  The first two are secreted rapidly and
eliminated rapidly.  The second two are secreted slowly and remain active for
4-6 hours, and may cause reactive hyperglycemia.

Neuroglycopenic responses are caused by decreased activity of the central
nervous system and are triggered only by low absolute bG levels; symptoms
include

   headache
   hypothermia
   visual disturbances
   mental dullness
   confusion
   amnesia
   seizures
   coma

The above information is from Mayer Davidson's _Diabetes Mellitus: Diagnosis
and Treatment_.

Remember, as always, that individual responses vary greatly. The exact set of
symptoms encountered will vary. It's not impossible that some of the symptoms
will fall in the other category for some individuals.