Putting Amethyst’s comment in to account, it is possible to raise a Pokémon speed stat to over 1000.
For example, Ninjask’s Speed stat with Max Speed EV’s and IV’s and a beneficial nature, is 460 (Source) and since the stat can be boosted four times the amount, Ninjask, after 6 turns, will have a Speed stat of 1840
Here is a list of the it’s speed at each stage
Stage 1: 690
Stage 2: 920
Stage 3: 1150
Stage 4: 1380
Stage 5: 1610
Stage 6: 1840
(This is for Ninjask)
With the speed boosts, it is well and truly possible for a Pokémon to get a speed stat over 1000. Probably most of the Pokémon with Speed can reach that extent if they have had a good amount of speed. It’s not only limited to Pokémon with that ability
Hope I helped!