My reasoning behind this is because my forum is currently on a vBulletin optimized host ($$$). The forum is running great and takes up very little space itself. However, the attachments (mostly all pictures) are starting to climb and occupy a lot of space on the server.
I was thinking if I could move just the attachments to a cheaper shared host (e.g. Bluehost shared hosting offers 100GB of storage for only ~$3.50/mo) then I can save myself quite a lot of hard-earned money instead of bumping up to the next tier with my current host - I really don't need any of the extras or performance it comes with besides the added space.
You will lose much of the pay off from being on a "Vbulletin Optimized" host by having your attachments remotely hosted. I understand why you would do it but you may be better just upgrading your server or pay for more space with them.