Just top expand a little on what Marc said.

in Encore save your menu as a PSD. Import this into Premiere (or your NLE of choice). Pop it on a timeline and then apply a fade-out filter of yoru choosing. Similar for audio.

Export this as MPEG2. Import the MPEG2 into Encore onto another timeline.

Now set your button press to play first the fade-out clip you just made and then your actual movie.

It will never be quite seamless (see any commercial DVD to prove it) but you button press will now appear to fade the menu away before playing your movie.

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