Do patella bones form in people born with the inability to walk?
In mice, patella would form, but not separate from femur.
On the development of the patella:

Previous studies have suggested a central role for mechanical load in
the initiation of sesamoid development.
Our finding that the patella initially forms as part of the femur and
is later separated by joint formation led us to revisit the issue of
mechanical contribution to patella development. To achieve this, we
studied patella development in mutant embryos devoid of contracting
muscles, as a result of the naturally occurring autosomal recessive
mutation muscular dysgenesis (mdg; Cacna1s). These mice lack
excitation-contraction coupling and, consequently, their skeletal
muscles lack contractility.
Histological analysis of sagittal sections of hindlimbs identified at
E13.5, in both mutant and control littermates, the existence of
patella progenitors, which were part of the femur. However, at E14.5,
whereas in the control we observed joint formation between the patella
and the femur, in mdg mutants this process was not detected.
Consequently, at E16.5 the mutant patella was still part of the femur.
These results suggest that, although muscle contraction does not
affect patella initiation, it plays a crucial role later during the
separation phase.

I know, you asked for human, but it is the only relevant information I found. However, while sources mention a role of physical stress in the calcification of sesamoid bones, the preceding formation of cartilage seems unaffected. Now, given the information that ossification occurs in mice without physical stress, I personally would conclude that the human patella would also calcify in paralyzed persons. Strictly, the question whether the patella forms, should be answered, if a non-detached patella counts.