Hi,
I don't know Informix but in case of other databases I can say that an ODBC connection usually doesn't lock the tables. But of course it depends on the way you are using the tables. If you only open them for reading then it doesn't disturb any write operations. If you write a record with Access usually the current changed record is locked - but only as long as it is written ("optimistic lock").
If this would not be the case then few users would be enough to dead lock each other working with the same data. Of course you can lock any database with opening the records or tables in the wrong mode but usually Access handles it as optimistic as possible so normally there should be no problem.
Simply test it, create a test database and access it with Access with more than one client.
Cheers,
Christian