Very very unlikely....
Working backwards; a heat pump is a type of heating system ... the reason for needing a heating system is not to heat the house per se but rather to replace the heat being lost from the house ... so if heat pump cannot replace the heat at the same or higher rate that it is being lost from the house then you will end up cold with very high electricity bills and likely a shorter lifespan on the hp.
Even if you got the house to a specified BER level, in my experience unfortunately a BER is not an accurate method to estimate the likely heat loss so cannot be relied upon for any form of comfort (excuse the pun) in this regard.
If you are embarking on a renovation / extension project then I suggest you take your time and research how heat is being lost from dwellings, the importance of air tightness & ventilation, the risks that internal insulation pose etc etc and try not to squander this opportunity to do it as best you can.