Yes, it is possible to solder potentiometers in place of the resistors. There are a few difficulties though.
1. The resistors values have to be pretty precise to get the correct internal signals and shape of the filter.
2. Small potentiometers like that cover their entire resistance range in only about 270 degrees of rotation which makes it quite difficult to get exactly what you want. You may think that it may just require a lot of careful effort but in many cases it is close to impossible with cheap single-turn pots as the value jumps around as you go back and forth trying to get the value you want.
3. Once they are soldered in you most likely cannot directly use a multimeter to check their value as you turn them because the other components in the circuit will affect the measured resistance. The best you can do is leave one of the outside pins unsoldered and measure the resistance from that pin to the center pin as you turn. You can then calculate what the value in the circuit is.
4. Cheap potentiometers often have very poor tolerance and aren't as good as discrete resistors over time and with temperature
If you're still set on having the SSF adjustable I would recommend 10-turn (or more) trimmer potentiometers like this.
Alternatively, if you know the range of resistance you need to adjust over, you may be able to get away with using two potentiometers in series. One for "coarse" and one for "fine" tuning the value. You could experiment with this by connecting say a 100K and 10K then practice changing to different values to see how easy it is before soldering. Just remember that once its in the circuit its more difficult to measure the value.
Thank you for a most excellent response. I was hoping to use the filter to shape low end response. Seemed like testing would be easier with a pot. I believe point #2 is the deal breaker. You reminded me of one previous attempt to set a pot to a precise level. Never happened.
I'm gonna get one for 25 cents, hook it to an Ohm meter and see how easy it is to adjust. Not much effort to that point. I think the 10 turn pot would be easier to adjust, but I'm not making a special order to get one. Maybe someone has one on hand and can tell us how hard it is to get a particular value.
That sounds promising. To adjust between 15 and 25Hz one resistor ranges between 50 and 90K and the other is 150 to 250K. I ordered the suggested 12 turn pot with values of 100K and 250K. It'll be fun to see what happens.
That should work out very well. Depending on the circuit you may not be able to measure the resistance while it is soldered in as I had mentioned before. To check this you can measure the value of the resistors currently soldered. If their reading matches what their colored bands suggest then you will be fine. If not, you will want to leave one of the potentiometer's pins floating in the air as a measurement point. You will then be measuring the ununsed section and can calculate the value (subtraction).
Before you solder the pot in measure the full resistance (outer pins). It won't be exactly 100K for example. Also turn it to about 1/4 1/2 and 3/4 positions and measure both sides. Check that they add up to close to the same value (~100K) for each position.
Then when it is soldered in, if you measure from the free pin to the center and get a reading of 75K that means that (100K-75K)=25K is what it is set to. The measurement taken before soldering will make this calculation more accurate. And since you're spending the money on the really precise 10 turn pots it would be a waste to not use this technique.