dhenry:
How likely am I to have problems without them?
Quite unlikely.
Sorry but dhenry is known here for giving compleatly useless and incorrect information. This pure gem is no exception. I can guarantee that you will have problems without decoupling capacitors. Even one chip needs them. Look at any data sheet and it will say the chip needs them. In my professional career over 80% of why circuits would not work was lack of enough decoupling, so there was decoupling in the circuit but not sufficient.
Even if a circuit appeares to function without one you will find the noise margin is degraded sufficiently such that it is no longer a reliable circuit.
Adding decoupling capacitors has cured about 80% of interment operations reported here.