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)
{
if (grid.InvokeRequired)
{
var pushAction = new Action<string[]>(myDataCls_PushData);
grid.Invoke(pushAction, someData);
}
else
{
DataRow row = dataTbl.NewRow();
row["Time"] = someData[0];
row["Name"] = someData[1];
row["Addrs"] = someData[2];
dataTbl.Rows.Add(row);
}
}