Yes - low pressure will stop the entire A/C system from functioning. Personally I have used KwikFit to re-pressure the system (approx £50) as if it doesn't work they do not charge. I have also had the actual A/C pump fail completely, but managed to get a salvaged one. You can get A/C pressure testing equipment - check out YouTube for how they work. This gives an indication if it is just low pressure or totally empty (which would indicate a leak).