When upgrading to SharePoint 2010 you have two paths; in place upgrade
or database attach. The answer to your question is different depending
on which of those methods you want to use. If you want to do an in place
upgrade then yes your SharePoint 2007 environment will have to be all 64
bit as you'll be installing SharePoint 2010 on them and it is 64 bit
only. In that scenario you'll be using the same hardware initially for
your SharePoint 2010 farm as you did for your SharePoint 2007. You could
add new servers later if you wanted to.

If you go the database attach route your SharePoint 2007 farm does not
need to be 64 bit. You can attach a content database from a 32 bit
SharePoint 2007 farm to a SharePoint 2010 farm. This method means you'll
need separate hardware, but it sounds like you already have that. It
also means you won't be upgrading your existing SharePoint 2007 farm so
you'll have to recreate in SharePoint 2010 any customizations you had in
SharePoint 2007.