I'm expecting they'll be away for a few weeks.
It depends on how busy Naim, or your chosen service place, is. The last time I sent something to Naim they didn't want it shipped down immediately. They waited until they were ready do the job before they asked for it to be sent down so the unit wasn't actually with them for that long. I think it was a couple of weeks.
Independants, all bets are off. My son had a few things fixed by a guy in Glasgow, no connection to any shop. He had a good reputation for being able to deal with tricky repairs but it took months and lots of hounding before he actually did the jobs. It was a Quad power amp and a mixer. I know another guy who was very well known and had a good reputation who told me himself that if he took a dislike to the customer he went into 'sleep mode' and made them wait.
Obviously I'm not saying that's the norm but Naim are clearly very systematic and professional. Naim servicing is also not
that expensive. Not saying it's cheap, and you can probably save money if you are getting a few units done, but if an independent repairer is doing a decent job you often find that they are not much cheaper than Naim. If you think about it, Naim do repairs as a service to their customers, they make money on product sales. Someone who just fixes things makes profit on that. I've called independants who've quoted me crazy money just to look at the thing!
And the parts used do matter. If you fit 'better' capacitors in a Naim amp it might change the sound but not necessary in a way you like. Not a good result if you've spent a lot of money on the servicing.
For Naim servicing my choice would be Naim or an approved naim service agent like Robert Ritchie, Witch Hat etc. You know that what you get back will sound right and will hold its value. That's my take anyway. Nothing is risk free but overall I feel that gives you the best odds of a good outcome.