I would be very surprised if you killed the asparagus.It usually  takes 3 years to get it all gone from a field.Round Up will curl it but not kill it with regular label rates.I would be very interested to hear how it does.I would think you have curled what is above ground but the next is coming on in a week or less.How you treat the fern after done cutting determines how it will produce next year. Were putting upwards of 1300 lbs fertilizer /ac before cutting with another shot after cutting.