Yes, tabular server supports .Net Provider but only for those Data Sources which are mentioned in this article –  Data Sources Supported (SSAS Tabular)

Take an example of Oracle, if you select Oracle in “Table Import Wizard” and click on Next, you will find Connect to an Oracle Database Windows -> on that windows select Advanced and it will provide  an option of Selecting Providers, if you notice in screenshot as follow you can see Oracle Data Provider for .Net is present.

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What about other data sources which are not appearing in the Table Import Wizard Relational Databases List, for such sources you can use Others (Oledb/ODBC)

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This option should work if you are able to connect to your Data Source using ODBC, I have tested with SQL Engine and it worked like charm and same manner I had tested with Hadoop (HDInsight) as well

2) If ODBC Providers supported by Tabular Server, then why its not working for me?

ODBC is supported by Tabular Server but you need to configure 2 DSN one for 32 BIT and second for 64 BIT but with same name, otherwise you will get an error message while importing data.

Why we need 2 ODBC DSN?

32 Bit is for SSDT and 64 BIT is used by Tabular Engine while importing data in Tabular Server, further explained in this post Post Link