Vdd rise test in real life
Do these capacitors hinder the high rise and fall time of the signal
generator because of their time constants?

Yes, the power supply decoupling capacitors will limit the rate in which voltage can rise unless you have a perfect pulse generator that has zero output impedance. It's a simple formula for most applications (no time constant): -
$$I = C\cdot\dfrac{dv}{dt}$$
So, if you have current drive of 1 amp into a 1 farad capacitor, you can expect the voltage to rise with a slope of 1 volt per second. If current is 1 amp and capacitance is 1 μF, then voltage will rise at 1 million volts per second or 1 volt per microsecond.

Can I still get a fast changing VDD in spite of the capacitors?

Not really because that is what those capacitors are there for. That  is the purpose for which they are fitted.