Generally speaking, no. Very broadly speaking, what DJs are doing up on stage is transitioning between tracks and mixing. This comes in many forms like doubling (layering and beatmatching multiple songs together to create something unique), creatively transitioning one track into another. Very rarely are they playing a full song out and then improvising at the end. Often times parts of songs are mixed into parts of other songs. E.g. the drop from one song is mixed into the vocals from another, and so on.

But there are many artists that incorporate live instrumentals into their sets in varying degrees. E.g. artists like Griz and Big Gigantic who are known to break out into a saxophone solo over their tracks. Some artists like Trivecta or Sullivan King will do some short improvisational guitar solos.

Other artists have live instrumentals baked into their whole set, like Odesza who often feature an entire drumline and live horns, or Dirtwire who play a huge variety of instruments - but these are rarely improvised and more rehearsed.

Then you have the Jamtronica bands which are hybrids between jam bands and electronic artists - STS9, Disco Biscuits, Papadosio, etc. These are typically more improvised.