The existing S61s are civ aircraft up until a certain point in the Transition to War and then the MOD effectively takes control of them, indemnifying the owner in the process. I suspect a similar arrangement will probably be put in place for SAR-H meaning that the MOD, in a conflict, can then strap guns, rockets or even Royal Marines to the side if they wish.
To be pedantic I don't think any UK SAR helicopter, mil or civ, can legally carry an ECMO team and all its equipment due to the presence of some nasty DAC that they embark with them. Nitric Oxide is a gas used in ECMO which is colourless odourless and if discharged into a confined space in sufficient quantity - fatal.