Absolutely! Especially in the Classical period, where the 1st & 2nd violins were seated on opposite sides of the stage.
This allowed for antiphonal effects like this easily heard one in the coda of the 4th movement of Beethoven 7 (about 50 secs before the end):
The effect of the 1st & 2nd violins tossing the motif back and forth would be audible in performances where the conductor uses antiphonal seating (1sts on the left, 2nds on the right). I went back to an old Klemperer recording & found that yes, the 1sts very clearly come out left speaker & the 2nds out of the right.
You will also find it in the orchestral & chamber music of other composers in the Classical period as a matter of style. Indeed, earlier musical periods also saw composers consciously use the placement of musicians for spatial effect: e.g. Gabrielli. And also in later periods composers were conscious of the spatial effect of performers, for example:
- Berlioz: Grand Messe des Morts - 4 brass bands placed around the hall
- Mahler: Symphony No. 8 - Solo soprano singing from the organ loft.
In your specific example, i think the effect that was more in Brahms' mind was the registeral contrast between the upper & lower strings. I would suggest that the throwing of the motif between left & right is an artefact of this recording in that Bernstein is using the modern string seating (v1, v2, va, vc, db). Had the seating been antiphonal (v1, db, vc, va, v2), the stereo effect would be gone, but (perhaps) the registeral difference emphasised.