When incorporating the STM32F7 MCU onto your own board design, is it necessary to connect supporting circuitry (analogue supply filtering etc) to the VDDA, VCAP pins if not using any of the analogue parts of the chip?
Yes. None of the STM32 chips I've worked with would boot without VDDA.
Check your datasheet (emphasis mine):
3.14 Power supply schemes
VSSA , VDDA = 1.7 to 3.6 V: external analog power supplies for ADC, DAC, Reset blocks, RCs and PLL. VDDA and VSSA must be connected to VDD and VSS, respectively.
Not much room for interpretation in a "must".