I've done this many times, and never emailed in advance. I'll mention it at check-in if I've already made them, but more often I get to the morning of check out, or a day before, make another reservation online, then drop by the front desk and ask them to link the two together and extend the keys. Only time I've had any issue was with some Chinese hotels booked through UK travel agents, where the front desk couldn't immediately see the new reservation. Even then, they called the hotel's reservations department and had it sorted within a few minutes.

The only real gotcha here is that they'll combine the two reservations into one stay credit, if that's important to you. This will happen even if you check out fully and back in to a different room.