Magento Go has since its introduction been a very restricted environment. It's nowhere near the level of Magento CE/EE, which are totally open-source. It's really not comparable to a competitor like Shopify either, which has an editable template system but fixed functionality.
This translates to pretty severe constraints on what can be customized in a modern, efficient manner (i.e. how you actually need to build a custom shop).
Magento Go ships with themes (less than a dozen last I checked), which are "ready-to-use". These were not designed or developed by Magento, but were outsourced to a third-party. This is critical to Part 3.3.
Themes in Magento Go are entirely constructed of CSS, JS, and images. There is no access to layout or template files like Magento CE/EE, which means you have to use the exact markup and functionality that Magento Go delivers.
You cannot add functionality except for "Trusted Extensions" which are vetted for Magento Go, but the selection is extremely limited compared to Magento CE/EE (where you could write your own of course).
You can only remove functionality that can be targeted by CSS/JS selectors, which is seems reasonable but is a major pain point because much of Magento Go's markup is not adequately described using classes for such targeting.
A 100% custom theme is possible (nothing is impossible) but entirely impractical. The primary reason is Magento Go does not have a "base" theme — that is a theme devoid of frontend stylesheets and JS behavior. To truly "start from scratch" that is what you need.
Magento Go requires you to pick one of its themes, and then customize on top of it. There are several reasons this is undesirable:
Assets from the underlying theme (JS, CSS, images) will still load, even if you don't want/need them.
You cannot blend layouts from multiple themes, it's all or nothing. So you're stuck with a theme's product view and category view.
The outsourced themes were written with very poor CSS standards. Their CSS is littered with inefficient and long selectors, and attributes are frequently defined with !important declarations. This is an absolute nightmare to override and maintain.
JS behavior is another story entirely. Each theme implements similar behavior differently like lightboxes. If you plan to introduce custom JS, then be aware you'll probably to unset events that are already attached.
There are commercial themes sold for Magento Go. These are not replacements for the core themes. They simply add on top of one of them, and suffer all the same problems.
Building something like a responsive theme is out of the question because Magento Go has locked in assumptions that don't hold up in that context.
Having said that
I have built a highly custom design on Magento Go (circa May 2011). It can be done fairly close to a stock/standard eCommerce site mockup with some concessions. I just don't recommend it.
Magento Go is good for somebody who just wants to pick a theme, add products, and sell — a one hour project. It's not a good platform for custom design. Shopify has nailed that already. For effectively the same price point they have a better product for custom design projects, and that is clear from the quality and breadth of Shopify's theme market.
But Shopify is still a hosted platform and that means constraints regardless. Complex frontend implementations would benefit from Magento CE/EE's strength behind the scenes (APIs / integrations / etc). Different platforms for different things.