Can a mixture of H2 and Cl2 explode if a spark is added?

Chlorine can serve as an oxidizing agent, that is, as an
acceptor of electrons from another element.  The scenario described in your question
would more likely produce an explosion of sorts if oxygen were present.  Oxygen is the
element by which what we would normally call "burning", or combustion, takes place.  The
chemical equation for the combustion of hydrogen is shown
below:

H2  +  O2 ---> H2O
(subscripts)

While it is possible to have the chemical
reaction take place between hydrogen and chlorine, it would not have the explosive
reaction described in the question.  The formulation of hydrochloric acid is a reaction
very similar to this:

H2  +  Cl2 ---> 
HCl