Is there a way that I can find out the Generated ID of the Selected Row
in a grid via Client Side script?

Yes, this is possible. You can use the following client-side function
(as the event handler for the OnClientSelect event):

function onRecordSelect(arrSelectedRecords) {    
    var iIndex = 0;
    for(var i=0; i<grid1.Rows.length; i++) {
        if(grid1.Rows[i].Cells[0].Value == arrSelectedRecords[0].SupplierID) {
            iIndex = i;
                break;
        }
    }
        
    var selectedId = getRowPrefix() + iIndex;
        
    alert("The selected row has the following ID: " + selectedId);
} 

// find out the row Prefix 
function getRowPrefix()
{
	var row0 = grid1.getRecordsIds().split(",")[0];

	if ( row0 != null)
	{
		var lastPos = -1;
		for ( var i = row0.length-1; i>=0; i--)
		{
			if ( row0.charAt(i)== '_' )
			{
				lastPos = i;
				break;
			}
		}

		if (lastPos > -1)
		{
			// get Prefix
			return row0.substring(0,lastPos + 1);
		}
	}
	return "";
}

(this assumes that the column storing the primary key - SupplierID in
this example - is the first column from the Grid)

You need to replace "grid1" with the ID of your grid.