I would work on the heart of the problem - Tune the data update queries to run faster.
Having said that, MS Access does not support multi-threading.
So, when you make a blocking call to a procedure, MS Access will freeze the screen until the call returns.
edit
DAO isn't really your best friend if you are updating a large table over a slow network connection. You might want to consider switching to using an ODBC connection and running a optimized update statement.
edit 2
when you use ODBC, you have to write ADO style code to make this work. Note this sample this code is OTTOMH.
dim myConn as ADODB.Connection
dim myCmd as ADODB.Command
set myConn = new ADODB.Connection
myConn.ConnectionString = "Provider=SQLOLEDB;Server=MyServerName;Initial Catalog=MyCatalogName;UID='XXX';PWD='YYY'"
myConn.Open
set myCmd = new ADODB.Command (myConn)
myCmd.SQL = "Update MyTable Set MyColumn = '" & MyDataVariable & "' Where MyPK = '" & MyPKVariable & "'"
myCmd.Execute
myCmd.close
myConn.close