I decided to see if I could find any research on this as I remember reading that asparagus hates weeds, and any plant in the row is going to act like a weed.
I found
https://acsess.onlinelibrary.wiley.com/doi/abs/10.2134/jpa1995.0035
Asparagus growth was reduced 50% in the first year and 25% in the second year when Asparagus seedlings were planted with clover. I read into that that you can indeed plant clover under your asparagus but wait until the asparagus is established before doing so. As a bonus they found that a mixed clover and rye grass cover reduced weeds to nearly 0 by the second year. that might be worth a 25% reduction in asparagus!
I sowed 150 asparagus seeds last year and had them in a nursery bed, I need to move them very soon to their permanent home, I'm planning on covering with half decayed woodchip, but maybe I
should try part of the row with clover. It would be an interesting experiment, I would probably have to label it well though so no one weeded them out!