Hi,
Yes, you can do storage VMotion and cold migration without VMotion network (because it uses management network for it)
Even I have tried both in my lab and it was successful.
you can read these links for more details: - Why is vMotion using the management network instead of the vMotion network?
VMOTION, STORAGE VMOTION AND COLD MIGRATION
These links should give good deep dive for VMotion. Please let me know if it helped you