No, you cannot create your own “Preset” that is stored within the Effect algorithm.

Those “Presets” are provided to help jumpstart programming your own Parts, for folks who are not accomplished audio engineers. Instead of just giving you a Reverb with a bunch of parameters to set on your own, you can quickly choose from a list of Presets made by our engineers and programmers.

“Basic”, “Small Hall”, “Clean”, “Church”, “Bright Hall” are, for example, the Presets for the “Rev-X” Reverb Type. If you know about Initial Delay, Diffusion, Room Size, and how to fashion the Decay and filters to recreate a specific environment, the “BASIC” Preset is the starting point. But creating a Church is more than just increasing the Room Size...

As the Effect processing found in the MONTAGE/MODX are boutique level, cutting-edge, these Presets are provided to give examples from which you can build. They simply recall parameter settings that you must then tweak to fit your own music... they are very general settings that shown the variety of character you can get from the parameters.

You will learn that with effects applied to music, the Presets only get you “in the ballpark”. There is no preset that works on every type of input... as the instrument, the type of music, even the performance on that same instrument changes, your opinion about the Effect setting may change. A Preset EQ for Kick Drum, for example, is only a recommendation. It will not work or sound the same on every drum. Those with Filters and EQs are specific to frequencies... changing the key of the music can change how the entire effect is working!

I’ve found most users are in too big of a hurry when setting Effects. If it is not right instantly, they choose a different effect... rather than work on their knowledge of getting the most out of the current Effect parameters. (That’s the drawback of getting too many choices...

What you get to do with the Effect Presets, is use them as General starting points.
When you STORE your data to the User Bank, your settings for that effect are stored with that Performance.
Insertion Effects are stored and accessible on a per Part basis... if you go and get the Part you will automatically bring along the Insertion Effect settings you customized for that Part. If you create an Electric piano with a specific Chorus and Phase shifter, you can always search for and recall that E Piano Part with its custom Chorus and Phase shifter.

It is possible to “search” for any specific Part from any Performance. Insertion Effects are technically apart of the instrument.
If your goal is to independently copy Effects settings (sans the Part they were used in), no.

Assuming you don't have some dedicated software to help you manage this, you could SysEx dump only the effects parameters to your Montage and save certain SysEx files for your own effect presets.

Focusing on only insertion effects:
Each PART has its own set of target addresses - so you'd need a different file for each PART (and one for A/D input). And then there's an "A" and "B" insertion effect - so you'd probably want a file for "A" and file for "B". To cover PARTs 1-8 plus A/D - this is 18 files per custom effect. If you're comfortable with scripting or programming - you could just create PART 1's SysEx file then automatically generate PARTs 2-8 by changing one byte of each address field in the original SysEx file.

On Windows, I would use MIDI-OX to transfer the SysEx file to Montage. I could also generate the SysEx file in MIDI-OX, although a hex editor may be another option.

This may be beyond what you want to ever do - but is the basic outline of one way to accomplish what you asked for.