As to my understanding Sharepoint 2010 will still work fine when TLS 1.0 is disabled for as long as TLS 1.2 is enabled. TLS 1.2 is the latest and more secured protocol although it has drawbacks when TLS 1.0 is disabled.
The older versions of browsers may not display as expected or not even display at all. UAT testing needs to be done for verification to assess on the result.
TLS 1.2 supports only the following browser specifications:
- IE11 and above is required.
- Mozilla Firefox version 27 and above is required.
- Google chrome version 30 and above is required.
Few points for to consider before disabling TLS 1.0:
- Microsoft Patch KB3080079 needs to be installed. This allows the user to continue using Remote Terminal Services or Remote Desktop after TLS 1.0 is disabled
KB URL: https://support.microsoft.com/en-us/kb/3080079
- Registry entry needs to be changed in the server.
- A server restart is needed for the configuration to take effect, so this means there will be a downtime for your site.
If anyone thinks that my answer needs some correction or it is totally wrong please let me know or please post your answer. I would be glad to know your inputs.