Like all hostile mobs they will fill up the mob cap, after the mob cap is filled the spawn rate is nearly zero.
As long as the mob cap isn't full other mobs shouldn't affect how fast slimes spawn in your spawner, but that probably isn't what you meant. ;-)
So technically the answer is no but for all practical purposes it's yes, you should stop ALL (or as close as you can get) hostile mob spawning outside your mob farm within 128 blocks of your position. That's a 256 block diameter sphere.
(You, of course, want to stop all hostile mob spawning altogether, in multiplayer you don't have much control over mob spawning near other players, in single player 128 blocks around you is all you have to worry about. )
I feel like everyone is having issues with slime farms lately, weird
This may have to do with a change in 1.14 that made all blocks, transparent or otherwise, affect the height range used when spawning mobs; that is, the game chooses a random y-coordinate up to the top of the highest block, so the spawn rate per layer will decrease as it gets higher (y=1 = 1/1 chance per tick; y=256 = 1/256 chance per tick). Previously, this was based on blocks that blocked light (1.14 introduced additional height maps where before there was just one, mainly used by light), so you could put glass over a slime farm and it wouldn't affect spawn rates (which also did not work prior to 1.8 since the game used the height of the highest loaded chunk section, so the mechanics in 1.14 are actually more like what the game used to have, except individual blocks are considered, not whole chunks):
Despite the title this affects mob spawning in general but is much more noticeable with slimes due to their low spawn probability, 1/10 of that of other common hostile mobs (1/2 at the surface in swamps).