That is correct, the alternative is to use a ($1000+) Server edition, some of which do give access to >4GB in 32b.
If you put 8GB RAM in a laptop running a 32b non-server Windows, you'll simply see 4GB.
You may see very small improvements nonetheless due to dual-channel activating (when pairing identical sticks of RAM, the CPU is able to "talk" to both at the same time rather than one at a time, doubling bandwidth), but I rather doubt it. The gains are usually insignificant. And you won't get any gains from actually increasing the amount of RAM in the machine.
So AD1066 doesn't need a 64-bit Windows, just any 32-bit Windows newer than XP.
No. Non-server 32b Windows will never give access to more than 4GB RAM to the user unless you patch the kernel. XP 32b, Vista 32b and 7 32b — including Ultimate for the latter 2 — all restrict "available physical memory" to 4GB in all situations. So do many server editions as well, for Windows Server 2008 x86 for instance, only the Enterprise and Datacenter editions will give access to more than 4GB RAM (up to 64).
A 2008 Enterprise license is ~$1500. I doubt ad1066 has any desire to pay such a price.
That being said, I still don't fully understand; Once I install the new RAM, will I only receive the benefits if I perform a new 64-bit install of Windows 7, or will upgrading just amplify the benefits? (I currently have 3 GB in 1 GB + 2 GB as the default factory configuration.)
Sorry if this question is dense of me, but my field is economics and the more technical aspects of HN are often lost on me