TortoiseSVN consists of 4 major parts:
1. An improved version of plink which you can use as standalone replacement
2. The Windows Explorer integration hack. This does little but build a popup menu and draw some fancy colours.
3. TortoiseProc which is called by the Explorer thingie. It does the "real" GUI stuff and the actual work.
4. TortoiseMerge, a standalone Diff/Merge application
You can call TortoiseProc from either a shell or from a selfmade little wrapper program, or you could make a shortcut to TortoiseProc with a commandline switch telling it what action to perform.
Either way, it will then present you with the well-known TortoiseSVN GUI, so you can select what to checkout or what to update.