In general, the answer is no. You can use some horn embouchures fairly successfully for trumpet, cornet and flugal but the variations in inner diameter as well as rim thickness will take getting used to. With a tuba mouthpiece you obviously use alot more of your lips but this is just a matter of learning one of the easier brass instrument to play - but the most difficult to transport. A Euphonium requires the development of different lip muscles as well as having plenty of breath support.
A further relevant complication, is that outside the UK Brass Band world, most ensembles expect lower brass instruments to read concert pitch parts (in bass clef) which is the same as transposing them at sight. In UK brass bands all parts are written in treble clef except bass trombone (and some percussion eg timpani) ie the parts are tranposed.
I say, if you've played one, you've played 'em all. The basic principal is the same, so the biggest problem would be simply getting used to the different sizes of mouthpieces.
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