Suppose the plane is in a thunder storm, and the pilot loses control of the airplane. Would deploying the ballistic parachute be a safe option? Meaning, is it likely that everyone would come out alive? Assume that as soon as the plane hits the ground at a reasonable speed the occupants are safe(as in, there's no ocean to drown in). Has this ever been done before?
Manufacturers are going to have different opinions of this scenario, but this answer follows the opinion of Cirrus Aircraft in their flight manuals and CCIP syllabi for the SR2X airplanes.
First off, your best bet is to obtain a proper weather briefing prior to departure and obtain in-flight weather updates enroute so you can stay out of a thunderstorm in the first place. The CAPS has very specific guidelines for operations as well as a maximum demonstrated safe deployment speed, depending of the model of aircraft. The flight manuals for the SR2X aircraft all state that:
"However because the CAPS is expected to result in structural damage to the airframe and, depending upon adverse external factors such as high deployment speeds, low altitude, rough terrain and high winds, the CAPS deployment may result in severe injury or death to the occupants and its use should not be taken lightly".
Barring that and you actually enter a thunderstorm which is so severe that it either causes departure from controlled flight or structural failure, there is a clause in the CAPS literature stating that if an accident is imminent, even if the acitivation of the CAPS is outside the demonstrated safe deployment range, it should be utilized and activated nonetheless. The reason has to do with minimizing the amount of energy on impact and even a partially deployed or damaged CAPS is going to slow the aircraft considerably, increasing your chances of survival.
Bottom line is that you did something stupid vis a vis a serious lack of judgment where a safe recovery is no longer possible. Whatever happens in the next few minutes is probably going to hurt really bad; the only thing we can do is make every effort to minimize how badly we are hurt and minimize the chances that we are going to be killed. Even an unsafe CAPS deployment in this situation is better than riding down to impact without.
In contrast, consider the success rate of another emergency egress aircraft system: The ACES II ejection seat USAF reports that in envelope success rate of ACES II is 94.4%, and combined in envelope and out of envelope success rate is 89.9%.
Out of envelope means the seat was employed in conditions it hasn't been certified for.
Success means the pilot lived, not necessarily uninjured.
So, first consider that these sorts of emergency parachute systems are not a 'safe' option, they're just considered better than guaranteed death.
As for the BPRS, it is not a 'safe' option under any circumstance. It is quite possible that the chute lines could get tangled up in the aircraft - remember that it will be deployed into a powerful wind, and in the event of structural failure, say a wing coming off, the aircraft might be spinning as it falls, tangling the chute lines.
Consider the fate of Vladimir Komarov, test pilot, aeronautical engineer, and cosmonaut. Faced with a failing Soyuz 1 spacecraft, he brought it into re-entry manually with almost no instrumentation and little ability to control it (an amazing feat), only to have the wildy gyrating capsule tangle it's parachute lines and impact the ground at high speed.
The BPRS would be considered a valid option, if the only other option was hitting the ground with no braking at all.
Deploying the BPRS in a storm would be essentially the same as making a parachute jump into a storm, subject to the same hazards, such as gusting winds collapsing the chute.
The only safe option for a light aircraft is to avoid storms completely.