Yes it will, if installed correctly.
Its pointless making general statements such as those you have made.
I have no problems maintaining 22 degrees C in our Valencia, in any weather we have been in, and it doesn't take 8 hours to warm up.
Indeed i have covered the heat exchanger behind the front chest of drawers because i was getting too hot.
Because these systems are piped in series its not possible to fine tune individual heat exchangers, as you can on a domestic system, helping to keep weight down is responsible for this, and costs.
If your install is poor because of the lack of radiators, then simply increase the CSA.
All the heat exchangers are is the pipe with push on fins, so simply convert your present interconnecting pipes to heat exchangers, alde supply the fins and can also tell you the KW rating per foot.
You mention Lunar, some Lunar have the in head circulating pump, which i don't rate, especially with a fixed bed as the noise from the pump can be intrusive, anyway i have heard of some owners getting the boiler mount pump, which i have which comes with a variable speed.
Mines set to position 2, and the system performs on that setting as expected, in fact i was considering reducing the speed to position one. It extends the pump life on a lower setting.
What i would suggest is that you increase the pump speed first, or fit the variable speed pump, Lunar should do this for you FOC, if you don't already have one.
See how that performs, if your problem persists increase the heat exchanger CSA.
If your problem continues it can only be a flow problem, ie partial airlock.
My particular model suffers from a cool bathroom, due in part from a undersized towel rail, which should have been a radiator, and the fact that the shower has a permanently vented roof vent.
Ps. our Bailey has plenty of space behind the seats and vents in the bases to allow airflow past the radiators, even the fixed bed has the same. And the wardrobes.