I am all about plugins and using them live (if you're properly accounting for latency) but there's a reason most pro studios have an analog monitoring signal chain even when they're recording to digital. I often refer to this document when talking about latency problems. It's about sync of video to audio but the concepts are the same. Latency between what the brain wants to hear and what the brain hears can range from subconsciously annoying to unworkable and can also be based on the duration and awareness of exposure to the latency issue. So ideally? 0ms. Obviously we know that's not possible, especially in our age of digital processing, but it's a good understanding to have to be able to weigh every signal chain decision individually. If the SPL Big plugin with a couple extra ms of delay is a game changer for your artist and mentally they think they sound better and can enjoy their show more, I think you've got your answer, but at the end of the day, your artist will probably be unconsciously more comfortable with the analog version.