The `Arokh HaShulhan, Hilkhoth Tefillin, siman 43:1-14, explains the laws relating to bodily functions and the proper donning/treatment of tefillin at those times.
Although the Rambam appears to be more mahmir and only allows one to urine in his tefillin under duress or if he forgot and began to relieve himself (see there), the Shulhan Arukh (and the plain meaning of the Gemara) indicate that - me-`iqqar ha-din - it is permissible to urinate while wearing tefillin in certain permissible locations (again, see there). It seems that the Hazal made a gezerah against it lest someone come to defecate or flatulate while wearing them, activities which are expressly forbidden.
Thus, it would seem that the unintentional possibility of urinary incontinence would not prevent one from wearing tefillin, at least during a time when they do not expect it to be likely to experience such incontinence.
The Gemara in b.Berakhoth 22b (cf. Rambam, Hilkhoth Tefillah 4:10) indicates that if someone experiences urinary incontinence during the Shemoneh `Esre he simply needs to pause until it stops before continuing. However, various Rishonim discuss the implications - le-qula - if urine is contained, splashed on one's garment, and/or covered by a clean, dry outer garment. Other Rishonim discuss this issue as well and most agree that urinary incontinence during one's tefillah is only a problem which requires action when one is aware of it and/or it drips or pools on the ground beneath him.
Thus, it would seem that a disabled person who wears an adult diaper could continue to pray even when experiencing known urinary incontinence, and all the more so when it is unknown.
What does this have to do with tefillin? Because the iqqar time to wear tefillin is during the Shemoneh `Esre (cf. Rambam, Hilkhoth Tefillin 4:26; b.Berakhoth 15a). And, since Hazal does not even mention the need to remove one's tefillin in a such a case of involuntary incontinence, it would appear that they are not concerned about it.
So, le-'aniytuh da`ati, it would seem that - pending certain reasonable details and conditions - the answer to this question is: MUTAR