False. Suppose a million gates switch with 1A in 100ps at 10nH of bond inductance? It’s 100V. If there is a lot of digital switching, local, on chip capacitance must be spread throughout the chip. Off chip capacitance for switching spikes, is useless. However… this question leads to sure follow-up advice…make sure you have digital power grounds, analog 0V power rails and analog reference grounds only meeting at ONE star point. It can not be stressed enough that analog 0V for POWERING analog blocks is NOT analog ground. Typically, you will need DIGVSS, ANAVSS, ANAGND, ANAREFGROUND, DIGVDD, ANAVDD, ANAVREF, and more, because there often analog signals that are pure accurate, references, with no or little current in them, and analog signals that have current, but that current should not corrupt other analog reference signals.  A mixed signal chip will certainly fail if the power and grounds are not done correctly.