I hope the question is not too stupid, as I am very new to Radio. According to my logic, the obvious answer is no. However I believe to have read somewhere that interference may be a problem when the second frequency is close to some multiple of the first? I do not know the exact bandwidths and have no way of testing the setup beforehand.
There is the possibility that one transmitter could de-sense the other's receiver. But it is difficult to predict - you simply need to try it.
To add to what Glenn W9IQ says, it depends on how sensitive the front-end of the receiving radio is. If it is not designed to be near strong out-of-band signals, then a strong out-of-band signal could 'swamp' the receiver's front-end, meaning that it can't process signals in its intended band properly because it is effectively overloaded.
As Glenn stated, it's not easy to predict. The best way to see how badly the receiver is affected by a nearby transmitter, is to try it. If transmitting causes intended signals to be wiped out, then that means that the receiver is affected.
The good news is that this is not too difficult to overcome - especially since the two frequencies are not harmonically related. You can put a good band-pass filter in line with the receiving antenna and that would cut out all frequencies outside the intended band. A properly-designed high-pass filter could cut out anything below 433MHz, and would be a simpler design. If the receiver is never used to transmit, then a filter would be relatively simple to make. If the receiver also transmits, then the filter would need to handle the power of the transmitted signal as well.
You seem to be thinking of harmonic distortion. A signal passed through an amplifier with harmonic distortion will add new signals at multiples of the original signal. For example, if the input is at 100 MHz, then there may be new signals at 200, 300, 400, ... MHz.
Any real amplifier will produce some degree of harmonic distortion, though in any properly working station it will be negligible. Usually the odd harmonics (in the example, 300, 500, 700 MHz, ...) are stronger when an amplifier has a push-pull output stage, which is very common.
So, harmonic distortion can not interference between 403 MHz and 433 MHz, since these numbers are not related by any integer factor.
Harmonic distortion is not the only mechanism that can cause interference, but it does seem to be the one you are thinking of. Intermodulation can also cause interference, though the frequencies where that interference appears is somewhat more complicated to predict since there are more unknowns.
And of course there are many other ways interference can happen. You ask if it's "possible", and strictly speaking the answer is yes. But it would be very unusual, and would require extremely cheap, poorly designed, or broken equipment.