It's NHS England that is being abolished, not the whole concept of managers in the NHS. As has been extensively hashed over on here, in any large organisation such as a hospital a certain amount of management has to happen, to keep the lights on, pay the bills, manage supplies, keep an eye on the money, ensure the organisation is compliant with the law, fix the PCs when they break, arrange essential training for the staff, make sure health and safety issues get fixed and so on. It's only ever in relation to the NHS do I seriously hear people suggesting that either this shouldn't happen (and so I guess the hospital just keeps working by magic I guess?) or that the front line staff should do this in addition to their regular job? Those seem bonkers to me. Now like in every single large organisation of course there is some chaff within the back office functions that could get cut alongside the essential stuff, and like with every single human (front line clinical staff included!) there are people who are super-humanly excellent at NHS management, people that are pretty good, people that are bang average, people that are lazy and crap and people that are so bad they're borderline dangerous and dragging everyone else down with them. If we could only identify and get rid of the bottom two tiers that would be excellent but incidentally you need a pretty good HR function to do that safely and fairly - another useless pen pushing set of people!
Back to your actual question, will abolishing NHS England make a difference and lead to more front line NHS staff? As a current NHS manager in a hospital (if you hadn't guessed!) I'd say yes and maybe. NHS England is a bureaucratic tier of management created by the tories to be between actual care-delivering organisations like hospitals and GP practices and the government. Previously we had similar but there were multiple regional bodies (NHS London, NHS South West, local primary care trusts etc). In theory not a bad idea as usually you can be more efficient by centralising and creating one big organisation out of multiple smaller ones, but it hasn't really worked IMO, it's gotten bigger and more bloated over the years bringing in more and more functions and more and more divorced from the reality of being on the ground. I also think it's lacking accountability as a body. However I wouldn't be so sure we can just take the huge NHS England budget and simply just put all that back into hospitals or front line care (bit like the old misleading brexit headlines). There's a lot of boring bureaucratic NHS stuff that someone is going to have to keep doing, whether that's the department of health, local care boards or hospital managers. E.g. in the last few years NHS England absorbed Health Education England into itself, that's the function that liaises with universities and colleges about placement management for student nurses and doctors, makes sure curriculums are up to scratch and oversees postgrad training for doctors, very complicated and important stuff. Now NHS have pretty much done a crap job managing all that and HEE were poor before then too so I'm not complaining it's going to have to move again but someone has to do it and ideally centralised at at least a regional if not a national level as it would be chaos if hospitals and GPs were trying to do it. Also, overseeing GPs, managing who is allowed to set up GP practices, performance managing them and deciding how much they get paid (and then actually paying them) is another complex job. At a guess I'd be saying even if you are very ruthless about cutting the more 'managerial' end of what NHS does (efficiency initiatives, patient safety promotion, equalities stuff), at least some of which I'd also say is worthy of attention even if NHSE didn't do the best job, you'd only save maybe 30% of the NHSE budget , and even if you did put that money direct into front line care, the NHS budgets as a whole are so small I don't think you'd see a huge difference when spread around the whole of the NHS.
TLDR = yes it's a good idea to get rid of NHSE, no it won't mean many more nurses on the wards.
Long answer to a short question but I hope you see how complicated these things are!