No, Pokémon Crystal is not capable of communicating with Pokémon Emerald.
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No, it is impossible to trade from crystal to ruby/saphire/emerald. The games are incompatible.
Trade it from firered and leafgreen to emerald.
Trade one from FireRed or LeafGreen. You can't get a Charmander in Emerald.
The first in game trade is in Rustboro City in Ruby or Sapphire you would trade for a Makuhita, however, in Emerald you can trade for a Ralts. NOTE - ALL OF THE EMERALD TRADES ARE BAD DEALS!
There is no NPC who you can trade a Haunter to for a Gengar in Pokemon Crystal. To get Gengar you will need to trade with another player or a copy of Pokemon Gold, Silver or Crystal.