While it's not perfect, it does provide official documentation that issues will arise.
Below is the whole context of the ticket we submitted for documentation on this matter.
Subject: RE: [REG:115061612850630] PREM B Business hours|SharePoint Server 2013|Want to have documentation/approval from Microsoft not use [$] dollar sign on the service account name
After researching internal documentations and Collaborating with my colleagues, it was determined that the most specific things that we can provide on this is the following:
SharePoint leverages PowerShell heavily in its functionality and PowerShell views the '$' character as setting a variable to be used in storing information. Once it sees the '$' character, it views the text following it as the Variable name that it is to store the data in or retrieve data from, that may have been stored in it previously. Based on this, and how SharePoint does not utilize quotations when it is passing in an account name to the PowerShell command, it would have issues in some scenarios where it is passing in an account name that has '$' in it as it will have issues since it will most likely see the name provided as a Null variable and not as the String type of data that would occur if the '$' were not used in the account Name.
Since SharePoint uses PowerShell so heavily and is running PowerShell commands in the background when using the UI or manually running command, the use of the '$' character in account names or service account names does not fall within the Microsoft Best Practices for SharePoint 2010 or higher.
We will assist with troubleshooting issues that arise from the use of the '$' character in the Account names, however, there are some scenarios that may arise where there is nothing that can be done to correct the issue that it can cause. We would support each separate issue in a 1-on-1 basis where each specific error or issue is handled in a separate service request.
You can go through the following links to read up more on PowerShell variables:
Outside of this, and the fact that the use of the '$' character is against Microsoft Best Practices for SharePoint, we would not be able to provide any more in-depth details as to why not to use it in the Service Account names.
Based on all of the testing that has been performed on this issue, that would seem like some of the specific scenarios that you would run into with the use of the '$' character in the service account name. However, the most that we can provide is to have a separate service request to troubleshoot why it is causing those issues to see about resolving them, without having to change the service account being used.
Please let me know if you have any additional questions or concerns regarding the above information