asmar, pde, p. 255 - as to the meaning of "y(0) is finite" used in that book, used in a proof of a theorem

if a condition is y(0) is finite, assuming some c1 is upon a term that is not finite (series), set c1 equal to zero on that term.

(the situation presented was some y = c1 y1 + c2 y2, y2 was a non-finite series and "deleted", meaning the condition was mean to read: y = y1 only in this case of this theorem)

that was in a theorem involving bessel J so it is not impossible it would be the same issue. issues of catalogued series solutions are ... delicate (how many solutions of what kind whether ln should be seen). it would be best to check your solution regardless.

Should I interpret the lack of replies to mean that the NDSolveValue function cannot handle a finite value boundary condition of the type described?

Please give more details and include any code you have already tried.