From memory, no I think that BBC2 (the channel it was originally shown on in the UK) made their own promo's for the show. But that is a very dim and distant memory of scattered bits and pieces.
They deserve to be made fun of though. From the melodramatic voice overs and wording. But as ever, the fact that episodic trailer materials frequently focused on action moments, explosions and phaser shots was actually less of a surprise than the cheesy way in which they actually did it.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist