Throw a smoke alarm up in your grow room. If you are really paranoid you can set up a fire extinguisher system too. Better to be safe, ya know.
A trip to your breaker box to identify the grow room circuit should rest your fears. Flip the breaker off make sure the outlet you want to use is dead by plugging in a lamp or something. Then turn it back on and label it clearly in the breaker box. The breaker should be marked with the load rating. Apply the math that Figong suggests above to prevent overloading the circuit. You should be good to go.
Any doubt, hire an electrician to test things out. Let him know you are installing a tanning bed, fish aquarium, stereo equipment, proabably shouldn't mention it's growing equipment.