Yes it would count as 30 amps, but you don't have to worry about going over the 200. Breakers panels are almost always "oversubscribed," that is, the sum of all branch circuits exceeds the trip current of the service main. That's no big deal, the assumption is that you won't be loading every circuit fully at one time.
In a Siemens panel, the stabs (the metal bars in the back that the breakers slip onto) come in two shapes. A complete stab services two slots, one on the right and one immediately opposite on the left. One is a solid metal bar, the other is a "U" shape, or more accurately, it has a notch cut in the center, about 3/4" across and deep.
The notched stabs accomodate tandem breakers. Unfortunately, you'll have to pull breakers out to see them, but you can do it carefully without disconnecting any wires.
I'm sure I don't need to tell you to stand on a dry board when working in the panel and to be very careful that you pay attention to where both hands are (no pun intended).
If all of your tandem ready slots are full, there are only a couple options left. One is to install a sub panel, which is a big job that most folks will hire an electrician for, and not knowing your experience level, I'd recommend to you.
Another option is to remove an unneeded circuit. A lot of people have a home wired for 240 volts for the stove, yet have a gas stove. If this is the case with you, you can remove the 240 volt range breaker all together and free up two complete slots. Just remove the red and black (sometimes both black) wires from the breaker, tape them good and shove them off to one side.
The other is to find a couple of equal ampacity (15 or 20A) circuits that are lightly loaded and consolidate them onto one circuit. Usually each bedroom is on it's own circuit, and almost never need to be, although I think code requires that they are. Use a wire nut and a small length of black wire (14 AWG for 15 amp circuits, 12 AWG for 20 amp) to connect the two blacks to one breaker. It won't cause a safety issue by doing this provided you don't mismatch amperages, but if you choose circuits which are heavily loaded you'll end up with an overloaded circuit breaker that nuisance trips. You MAY (don't know for sure) violate code by doing this, so a home inspector will make you fix it if you every try to sell the house.
Don't consolidate breakers for fridges, microwaves, washers, furnaces, or dishwashers, or kitchen circuits. Code requires that these be dedicated.