You can get a client-side "hook" when the update panel is about to fire. This means that you could, at least, temporarily disable the text boxes (or have some sort of 'please wait' notification) while the update panel is refreshing.
The following snippet of ASP.NET/Javascript shows how to intercept the update panels firing and disable the textboxes.
<form id="form1" runat="server">
<asp:ScriptManager runat="server"></asp:ScriptManager>
<div>
<asp:UpdatePanel runat="server" ID="updatePane1">
<ContentTemplate>
<asp:TextBox runat="server" ID="textBox1" AutoPostBack="true" OnTextChanged="textBox_TextChanged" />
</ContentTemplate>
</asp:UpdatePanel>
<br />
<asp:UpdatePanel runat="server" ID="updatePane2">
<ContentTemplate>
<asp:TextBox runat="server" ID="textBox2" AutoPostBack="true" OnTextChanged="textBox_TextChanged" />
</ContentTemplate>
</asp:UpdatePanel>
<br />
</div>
</form>
<script type="text/javascript">
Sys.WebForms.PageRequestManager.getInstance().add_initializeRequest(InitializeRequest);
function InitializeRequest(sender, args) {
if (args._postBackElement.id == 'textBox1' || args._postBackElement.id == 'textBox2') {
document.getElementById('textBox1').disabled = true;
document.getElementById('textBox2').disabled = true;
}
}
</script>
I know this isn't exactly what you originally asked for ("is there a way to queue postbacks with UpdatePanel"), but the net effect is that it forces the user to queue up their requests so no more than one is being processed at a time. You can probably amend this to something more elegant too.