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Sure, you can take a point from the ambient projective space and do a membership test:

sage: PP.<x,y,z,w,u,v> = ProductProjectiveSpaces([3,1],QQ)
sage: W = PP.subscheme([y^2*z-x^3,z^2-w^2,u^3-v^3])
sage: PP.point([1,1,1,1,1,1]) in W
sage: PP.point([1,1,1,1,1,2]) in W

Internally this does a try - except block around W.point(...).