Client would like to switch to Magento, specifically to Magento Go from currently used custom made webshop solution. Would it be possible to integrate Magento Go with this "in-house" system to use some of it's features - apart from writing the module and uploading to Magento Connect so that it may be installed from there?
It's not possible to upload custom modules to be used in Magento Go stores. There are a limited number of Go extensions: http://www.magentocommerce.com/magento-connect/catalogsearch/result/?q=&pl=3&te=1
Without more knowledge of the type of integration you're hoping to implement you'll probably have a hard time or find it impossible to do so.
No it would not. No tools or packages exist to do this, and the amount of custom programming needed would be tremendous. Additionally, the only interaction Go allowed is via its API — you can't create MagentoGo extensions.
Finally, I used "allowed" above because Magento Go's been discontinued. Ebay will be shutting it down later this year.