This won't add the frequencies in the way you're probably expecting.
A comparator is a nonlinear element. This is a special case of a more general truth: when waveforms are added together in a linear circuit, they obey superposition: it's just that, the result is the simple sum of the inputs. When the sum is passed through a nonlinear circuit, however, superposition is broken, and the result is not the simple sum, but contains product terms (which contain sum and difference frequencies, harmonics, and harmonics of the sums and differences, and so on).
The simplest (textbook) case is a product of two sines (y = (sin wt)(sin vt)), or the square of the sum of two sines (y = (sin wt + sin vt)^2). In either case, we can use trig identities to simplify the result, and observe that the frequencies w and v add and subtract.
A triangle wave is a bunch of sine waves stacked up in a particular manner. That is, we can take the Fourier series of the triangle wave, and look at the superposition of sines (harmonics). When this wave is sent through a nonlinear circuit (the comparator), the harmonics are mixed in this way, and a different result is obtained (namely, a square wave of some duty cycle; the harmonics of which, generally go as 1/n when n = odd and zero otherwise; but a variable duty cycle promotes even harmonics and puts a sinc(f) envelope on them corresponding to pulse width; okay so this is technically correct, but for simplicity's sake, suffice it to say, it's just some kind of square wave).
The sum of two (orthogonal*) triangle waves, will indeed cross zero (or for two biased (0-5V) triangle waves, cross 5V -- it's just an arbitrary threshold, might as well center things around zero for argument's sake here), (sum of frequencies) times per second. So the comparator output will be a square wave with those zero crossings.
But notice what the one triangle is doing to the other. Think about one triangle varying very slowly. It's varying the threshold the other one is being compared at: it's making PWM. You will indeed get one extra pair of edges, every cycle of the slow wave; but the edges aren't evenly distributed. The one frequency remains, as does the slow frequency (we've made a PWM modulator -- it could just as well be used for, say, audio reproduction!), and the sum and difference, and their harmonics. It's a very messy process, if all you wanted was the sum and difference!
*Meaning, the frequencies don't match up in some relevant way. They aren't harmonically related, say. Or, at least, the ratio is an odd enough number that we can't measure it very easily.
Tim