Yes and no: that isn't how SQL Server on Docker works... Try it for yourself:
$ docker run -d -p 1433:1433 --env sa_password=abc123 microsoft/mssql-server-2016-express-windowsThat requires you to be running Windows Server 2016: https://github.com/Microsoft/sql-server-samples/tree/master/...
Essentially, they have a docker-API-compatible HTTP server that runs a different set of container images. Similar to how SmartOS has a docker-API-compatible HTTP server (running on top of, essentially, a Linux emulation layer).
Well yes, that was my point. No sign of VirtualBox running Windows inside Docker there...
In short: VirtualBox is still probably the best option for running those IE VMs, and for cases like this Docker is not really a replacement for or competitor with solutions like VirtualBox.