In case of you have not try this yet, you can customize "TubePoints", CapForm and JoinForm to reduce the FrontEnd memory usage. By default value of "TubePoints" method option is {40, 2}, and the default "Round" CapForm and JoinForm involves more sampling. Since you have a lot of small tubes and reducing sampling won't affect too much your visual results, you definitely should give it a try.
Graphics3D[{Tube[RandomReal[.1, {50, 50, 3}],
VertexColors -> RandomReal[1, {50, 50, 3}]]}]
Graphics3D[{JoinForm["Miter"], CapForm["Butt"],
Tube[RandomReal[.1, {50, 50, 3}],
VertexColors -> RandomReal[1, {50, 50, 3}]]},
Method -> {"TubePoints" -> {5, 2}}]