That is a purely mechanical and unrelated effect you are describing there - and one which the observer falling into the black hole would himself observe - long before he achieved relativistic velocities. Actually, tidal forces (or more accurately: differential gravitational forces) would tend to form whatever object falls into a black hole into a conical shape.
Regards,
To an observer watching something falling into a black hole would see it spaghettify...I forgot that. thanks for the correction