If you connect 1 pullup resistor to the analog mux output rather than 16 resistors on each mux input, it can work but you will need to allow more time between switching the mux control pins and reading the signal.
Those mux chips have on resistance in the range of hundreds ohms. Teensy is very fast, so even with just the mux resistance and the capacitance of its pin and Teensy's pin and the ADC input, you will need a brief delay after changing the mux control signals to allow the voltage to settle before you read it.
The pullup resistor is 10,000 ohms, about 25X more. So if you had the mux selected to a pressed pushbutton and you chance it to one that's open, you must allow enough time for the 10K resistor to slowly bring the mux output voltage back up to logic high.