TTL is really a family. CMOS is Complementary Metal Oxide Semiconductor. You can have a CMOS OP amp. CMOS is more of a generic term.
See:
https://en.wikipedia.org/wiki/Logic_family
For a list of some logic families. The "FAMILY" has a set of characteristics. The one thing that's usually defined is what is a high and what is a low and Typical FAN OUT (How many gates will an output drive)
CMOS only consumes appreciable power when switching. When an output is at logic 1 or zero nearly no power consumed.
Some of the early computers I worked with used DTL and RTL logic.
The HCT logic family has the Hi/Low levels of TTL logic and the low power and output characteristics of CMOS.
"pull downs" would not be called a pull down in an analog circuit, but they would exist. As an example to set the input Z of an amplifier too 600 ohms, a 600 ohm resistor is placed from the input to ground.
On a non-inverting amplifier, the (-) lead is attached to ground through a resistor. It' doesn't have to be, BUT it improves bias current compensation.
Capacitors, since they are not idea, may require resistors to drain them of excess charge.
Since OP amps can be used as comparators, you could pull-up the output or with the addition of a diode and a pull-up convert it to an Open Collector output.
So, in a sense, yes.