I found this tutorial and looks like it is quite possible.
http://kogzee.wordpress.com/2013/08/07/style-sharepoint-2013-top-navigation-global-navigation-menu/
EDIT
The above article explains how you can integrate your custom menu with SharePoint in 2 easy steps.
Suppose you have got the CSS and HTML of menu from designer and now as a SharePoint developer you want to integrate it. Here's how CSS and HTML file will look like:
CSS
The CSS is pretty large so I am only pasting small portion of it. You can see rest of it on the link above.
/*Navigation*/
.crom-Navigation {
font-family:"Trebuchet MS", Helvetica, sans-serif;
margin: 10px 0px;
top: 0px;
position: relative;
z-index:200;
}
.crom-Navigation a {
margin: 0px;
padding: 0px;
border: 0px;
text-decoration:none;
}
.crom-Navigation ul {
list-style: none;
margin: 0px;
padding: 0px;
font-size: 16px;
z-index:200;
border-bottom: 2px solid #003f5f;
}
HTML
<!--Menu-->
<div id="navigation" class="crom-Navigation">
<ul>
<li><a href="#">Cameras</a>
<ul>
<li><a href="#">Camcorders</a></li>
<li><a href="#">Digital cameras</a></li>
<li><a href="#">Disposable cameras</a></li>
<li><a href="#">Film cameras</a></li>
</ul>
</li>
<li><a href="#">Computers</a>
<ul>
<li><a href="#">Desktops</a></li>
<li><a href="#">Laptops</a></li>
<li><a href="#">Netbooks</a></li>
<li><a href="#">Tablets</a></li>
</ul>
</li>
<li><a href="#">Media</a>
<ul>
<li><a href="#">Movies</a></li>
<li><a href="#">Music</a></li>
<li><a href="#">TV shows </a></li>
<li><a href="#">Video games </a></li>
</ul>
</li>
</ul>
</div>
Now simply do the following steps and the menu will be displayed.
Call that custom CSS in your master page
<SharePoint:CssRegistration
name="<% $SPUrl:~sitecollection/_catalogs/masterpage/CromwellFixedWidth/CromwellFixedWidthStyle.css %>"
runat="server"
after="SharepointCssFile"/>
Copy/Paste following code in your master page where you want to display menu
<!--Menu-->
<div id="navigation" class="crom-Navigation">
<!--Top Menu-->
<SharePoint:AjaxDelta id="DeltaTopNavigation" BlockElement="true" CssClass="ms-displayInline ms-core-navigation" role="navigation" runat="server">
<SharePoint:DelegateControl runat="server" ControlId="TopNavigationDataSource" Id="topNavigationDelegate">
<Template_Controls>
<asp:SiteMapDataSource
ShowStartingNode="False"
SiteMapProvider="SPNavigationProvider"
id="topSiteMap"
runat="server"
StartingNodeUrl="sid:1002"/>
</Template_Controls>
</SharePoint:DelegateControl>
<asp:ContentPlaceHolder id="PlaceHolderTopNavBar" runat="server">
<SharePoint:AspMenu
runat="server" UseSeparateCss="false"
AdjustForShowStartingNode="False" StaticDisplayLevels="2"
AccessKey="1" SkipLinkText="" EnableViewState="False"
MaximumDynamicDisplayLevels="1"
DataSourceID="topSiteMap" Orientation="Horizontal"
RenderingMode="List"
UseSimpleRendering="False"
ID="TopNavigationMenu">
</SharePoint:AspMenu>
</asp:ContentPlaceHolder>
</SharePoint:AjaxDelta>
</div>