Paralysis to my understanding is protected under laws regarding handicap and I'm unsure how it would apply in regards to a situation like this and the type of argumnent that's ACTUALLY used rather than the hyperbolic one used by the OP. In regards to the OP's, yeah it'd likely clash with it despite the whole disabilities protection thing. Based on what the argument ACTUALLY typically is, I'd go no (see my comments above regarding broad coverage, high efficiency, deferment to recognized rights).
Which, as I pointed out earleir, makes the system and the goal of what you're striving for inefficient by allowing a siginficantly larger pool of people who are counter to the (as stated by the premise) goal of the act.All SSM does is treat marriage exactly as it is treated in these two-gender instances where child production is known to be totally impossible without 3rd party intervention.
To put it into numbers, if you want it broad and efficient and assuming both take the same amount of work to discover:
If you can allow 100 people in and 10 of those 100 are not what you're looking for then you have essentially a 90% efficiency rate.
If you can somehow bump it up to allowing 150 people in but 60 of those people are now not what you're looking for then you've reduced your essential efficiency down to 60%.
Now you could perhaps only let 90 people in and weed out those 10, but doing so would also potentially be less efficient as you'd then have to research each individual beyond a simple test to see if they qualify as well as potentially invade individuals privacy.