For all the more that is visible in a Healey engine bay, basically the fire wall, I would be more concerned about how exactly I would approach the job at hand. With all the cables, hoses, grommets, brake lines, etc. that are in the way, there will be an extensive amount of taping and masking involved to come close to the effect that I'm sure you want to achieve. Spray cans are one of the least effective methods for applying paint, second only to a brush. If your person is mixing color, one has to assume that the quality will be considerably better than your average rattle can. You should be able to keep the paint wet and get it to flow, but aerosol propellants and more specifically the nozzles don't generally give a steady flow of paint. Compound that with trying to paint around all of your obstacles and I believe you are looking at disappointment in the final result. If you would decide to remove all of these obstacles, which would be a rather extensive job, then it would be a considerably easier task applying the paint. But to go to that extent would warrant doing the job properly and with the right equipment.
Most likely, that color match will not be perfect factoring in enamel vs. lacquer, and primer color but it should be close enough.
I would also have your paint guy mix up a good primer. Scuff everything down with a Scotch Brite pad and follow up with a wax remover/degreaser, all available at your paint supplier.
Will it be as shiny as your exterior paint? No. If your car has been painted with lacquer, it has been wet sanded and buffed to achieve the shine. This is something you won't be able to do effectively to you engine bay.
I hope I have given a little insight to your question.