I don't believe you will based on the limited scope of your sharing. The one operation is adding new records. And the other is changing. You could have a race condition where an enumerator misses a check on some of the new rows, but it should pick it up later since it's on a timer.
I would recommend looking at the algorithm, because it seems pretty inefficient to enumerate all the rows continually.
Also, here's a better way to invoke back on the UI thread that doesn't duplicate code (you may have to tweak it since I'm doing it by memory):
private void myDataCls_PushData(string someData)
var pushAction = new Action<string>(myDataCls_PushData);
DataRow row = dataTbl.NewRow();
row["Time"] = someData;
row["Name"] = someData;
row["Addrs"] = someData;