The answer is yes - you can sail a Hunter RTW, but you will not go round in the same level of comfort and safety
as a bluewater boat, and it might not even work out cheaper.
Taking just one example: Your ground tackle: probably not enough chain, probably the anchor
is too small, probably the windlass
is too small, probably the bow roller is too flimsey.
Now you can go RTW with this, but you won't sleep very well and there is a much higher change that you will loose your boat one night when 40-50knots comes throught the not-so-great anchorage that you will stop in from time to time.
So you have the choice of replacing all this before you leave (it's not looking so cheap
now..) or take a higher risk of loosing your boat.
Taking each system on your boat and assessing it's "fitness for purpose" you will quickly realise that the boat has been designed for light contitions and marina life (as most production boats are - that's the market).
Taking a production boat RTW is like taking a small towncar off road. It can be done, a few have even done it sucessfully, but it really isn't what it's designed to do.