There is no harm in asking the person at the end of the phone what the situation is. They are likely to be the same person who answers the phone when you make a claim, so if they tell you now that by installing your own kit you've voided your cover, you'll get the same answer in the event of a claim. Especially if the hardware you're claiming against isn't what they have recorded in your account!
Also, your comment about communication between an engineer and the telephone operator... No engineer worth his salt will rely solely on the comments taken by the phone operator. They are not technical and may not be able to accurately reflect your problem in text. Therefore any decent engineer will always start from scratch and ask their own questions to work out your view of events and dig to the bottom of your problem.
They will also probably ignore you if you say you've already tried some troubleshooting and will try the same themselves. If they haven't seen it with their own eyes, it's not true....
In my experience, I paid for Sky+ and then installed my own SkyHD box. The box was brand new and well within warranty, but as it was technically second hand the warranty cover didn't apply. I bought protection via Sky and told them this (it was obvious though, given the fact they hadn't installed it!) and they said the would happily cover it but on 'out of warranty' terms... which meant a 30 day wait before cover began but otherwise similar cover.
So my point is call them and ask their advice, as you could well be covered still