For a custom race you only seem to get the choice of the existing faction start star systems at the moment, so I don't think so unless a dev. tells me otherwise at least not currently.
Even modding it looks problematic as it appear that to appear in the list it has to be added to the FactionStart StarSystemGroup which it seems you can only do by making an override version of the StarSystemDefs.xml to your mod since a StarSystemGroup InternalName must be unique so you can't add to the list from a separate file.
At least it looks that way based on what Dumhead has been trying Mod wise.
Are there any devs who can give us insight here, is that correct?