No it will not work. Firstly, the SAW will try to maintain the frequency, that's why they are usually used on AM (OOK) systems. Having said that, they can be pulled slightly by adding additional capacitance across them. The second reason is the difference in fundamental, fundamental + modulation and fundamaental - modulation is far too close to be able to filter out the ones you don't want. When signals are mixed they should be sufficiently far apart that the by-products can be separated by filtering. With only 10KHz (2 x modulation frequency) difference between the +/- carriers at best and virtually no reduction in the fundamental you have almost no chance of isolating just the one you want.
As the modulation frequency is so low it would probably work if you just pulled the SAW frequency using a variable capacitance diode. The concept is you connect a fixed capacitor (for DC isolation) and a varicap diode in series across the SAW device. The varicap should be reverse biased by a small DC voltage to make sure the modulation voltage never drives it into forward conduction. You supply that voltage through a high value resistor (>10K), because the diode is reverse biased there will be almost no voltage dropped acrss the resistor but it will act as a barrier so the 433MHz oscillations are not damped by the power source. You apply the modulation signal through another capacitor (again for DC isolation) and another resistor (for RF isolation) in series to the varicap diode. The DC you apply sets the capacitance of the diode and the modulation voltage mixed with it makes the capacitance change according to the modulation signal. This detunes the SAW so it's frequency shifts and produces the FM you are looking for.
It sounds more complicated than it is, all you need is two resistors, two capacitors and a varicap diode, probably fewer components than your original mixer idea.
Brian.