Short answer - Yes, either type of LNB will work with the new Freesat 4K boxes.
A bit more info if you're interested. You'll get slightly different results with how many channels can be recorded between your Q LNB and the standard Quad LNB at the 'rents.
Freesat/Sky satellite signals are grouped in to 4 bands. Two of the bands have the bulk of the channels split between them. The other two have fewer. A single output LNB switches between the four bands subject to a bit of voltage and polarity on the feeder cable between the box and the LNB. When you change channel, the box tuner will either look for that new channel from the band it is already receiving, or it will change the LNB to a different band.
So far, so simple. If you want to watch or record another channel then you need an extra LNB and tuner to drive it. This avoids the problem that sometimes the channels will be in different bands. Rather than just doing a twin output LNB Sky went for four LNBs in the same housing; hence the Quad LNB. That gave them enough outputs to run the dual-tuner boxes and provide two spare.
When you plug in the 'rents LNB feeds to the new Freesat box you'll get the familiar 'watch one / record another' facility as Sky+HD.
SkyQ uses a different type of LNB. It's called a wideband. It works very much the same way as a TV aerial in that you get all the channels down a single wire. The new Freesat 4K boxes recognise the wideband signal and change how they they work. When you connect two feeder cables the box flips over from two-tuner-mode to 4-tuner-mode. This means that if you're happy to leave the box in standby, or watch one of the recording channels live, or play a previous recording, then it's possible for the box to make four recordings simultaneously. That's handy if you're going on holiday and want to avoid timer clashes.
In most cases the 4K box with wideband LNB will be used as the main TV tuner, so in reality you'll watch one channel live and be able to record three channels even if all the timers overlap.