Your blood pressure and getting that sorted is more important for now, but as an academic, I have immersed myself in some of the academic research on VLCDs and can say that in some or many of the articles, people are reported to see an improvement in both systolic and diastolic BP and can come off medication or take a reduction.
My personal experience is this: at 19 years old I visited the GP with very bad sinusitis and was checked over; she found I had high BP (could have told her that... I had been waiting for half hour to see her and was almost sick with nerves, always am where medicine is concerned). She was very concerned because at this time, yes, I was about 16 stone but at 5'10" that was not a drastic thing and I played netball at county level and hockey at local level; I swam 5 nights a week and I regularly played badminton and went to the gym, plus I had my horses. You could say I was very active (still was til I got ill this year and put on 5 stone). So she referred me to a consultant; meanwhile she put me on atenalol which really badly affected me, making me really dizzy and sick. The consultant appt came a few months later and here I was tested through xrays, scans, ECGs, BP and all the rest, and then given a 24 hour BP monitor to wear into the next day. When I saw the consultant my BP was 200/105 (he was fit!) and he was duly concerned, but when my monitor came back to him the next day, he was even more concerned that both levels were below 100 (only the diastolic should be). Basically, I was diagnosed with white coat hypertension, meaning a visit to the doctor sends my BP rocketing. The tablets had made my BP even lower and I was taken off them immediately (too quickly). Strangely, seeing the nurse doesn't affect me like this so whenever my GP does a reading and it is high she refers me to the nurse in a few days' time. So it is not always a true reading you see, especially if you know you get nervous. I have had several 24 hour monitors since then and I am a long sufferer of low BP.
With regards a reduction in BP on this diet: as you lose weight your heart has to work less vigorously; also, as you have seen a downturn in salt intake (you should supplement your packs with salt as we do need it in our diet and there is none in the shakes), your blood pressure will decrease. Any increase in activity will help your heart also and will decrease BP.