I came to know that, some master pages like BlueTabs, BlueVertical etc... didn't support treeview in Quick-Launch by default, even if tree view is enabled.
I got an idea of customizing methodology from this "Replacing the Menu Control with the TreeView Control" content, listed in this site.
But I received a binding error after replacing this code.
I went through the same and did following code changes and the quick-launch menu is customized to Tree-View and now it is working fine.
Below is the code.
<Sharepoint:SPNavigationManager
id="TreeViewNavigationManager"
runat="server"
ContainedControl="TreeView">
<table class="ms-navSubMenu1" cellpadding="0" cellspacing="0" border="0">
<tr>
<td>
<table class="leftNav" width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td nowrap id="idSiteHierarchy">
<SharePoint:SPLinkButton runat="server" NavigateUrl="~site/_layouts/create.aspx" id="idNavLinkSiteHierarchy" Text="View All Site Content" AccessKey="<%$Resources:wss,quiklnch_allcontent_AK%>" CssClass="leftNav2" />
</td>
</tr>
</table>
</td>
</tr>
</table>
<div class="ms-treeviewouter">
<SharePoint:SPHierarchyDataSourceControl runat="server" id="TreeViewDataSource" RootContextObject="Web" IncludeDiscussionFolders="true" />
<SharePoint:SPRememberScroll runat="server" id="TreeViewRememberScroll" onscroll="javascript:_spRecordScrollPositions(this);" Style="overflow: auto;height: 400px;width: 150px; ">
<SharePoint:SPTreeView id="WebTreeView" runat="server" ShowLines="true" DataSourceId="TreeViewDataSource" ExpandDepth="0" SelectedNodeStyle-CssClass="leftNavSelected" HoverNodeStyle-CssClass="leftNavHover" NodeStyle-CssClass="leftNav2" NodeStyle-HorizontalPadding="2" SkipLinkText="" NodeIndent="12" ExpandImageUrl="/_layouts/images/tvplus.gif" CollapseImageUrl="/_layouts/images/tvminus.gif" NoExpandImageUrl="/_layouts/images/tvblank.gif">
</SharePoint:SPTreeView>
<SPLinkButton runat="server" NavigateUrl="~site/_layouts/recyclebin.aspx" id="idNavLinkRecycleBin" ImageUrl="/_layouts/images/recycbin.gif" Text="<%$Resources:wss,StsDefault_RecycleBin%>" PermissionsString="DeleteListItems" CssClass="leftNav2" />
</SharePoint:SPRememberScroll>
</div>
</Sharepoint:SPNavigationManager>
I hope, this content will be useful for many users, who are trying to customize the quick-launch in Master Page to Tree View.