Answer : YES, The precipitation reaction will occur.
Explanation : When we mix the aqueous solutions of Lead chloride and Ammonium sulfide a reaction will occur which is stated below :
[tex]PbCl_{2} +(NH_{4}) _{2} S ----\ \textgreater \ PbS + 2[ (NH_{4})Cl] [/tex]
The major product that is formed is Lead sulfate which is black in colour.
Once the reaction is complete one can observe a black precipitate getting obtained.