Will I face any compatibility issues when I use MA 2010?
It's not possible to create Web Access databases in SharePoint 2013. It is, however, possible to continue to use a Web Access database created in a 2010 environment. So the answer to your question is; it can't be created, but you can continue to use web access databases created with SharePoint/Access 2010.
Access web databases are supported for backward compatibility
By default, you cannot create a web database by using Access 2013. However, you can still view and edit a web database that was previously created by using Access 2010 and SharePoint Server 2010, and you can republish it to SharePoint Server 2013.