If it was long-acting insulin as opposed to fast-acting, no you wouldn't necessarily test beforehand. And you definitely wouldn't have to eat or drink anything as mega sugary as Lucozade, yes lots of us use it for hypos. 10 ml of it is 17g or carbs, which would increase my BG by almost 6.0. So a whole bottle of it would kill me, without insulin. I would have to inject 6 units of fast-acting insulin to 'get rid' of 10ml of Lucozade, if I just drank it willy nilly and not just when hypo.
For a T1, slow insulin is injected once or twice a day, and takes care of our background needs - ie to keep our hearts beating, our lungs breathing, our instestines working, our brain funstioning - all the things nobody ever thinks about needing insulin. Then if we eat something with carbs in it, we have to take fast insulin to 'cover' that.
There is also a 'mixed' insulin which some people (more T2s than T1s) which as the name suggests has a mixture of fast, slow and even intermediate!
With regard to insulin, many T2s have some or a lot of Insulin Resistance, which you probably know about? - that means any insulin wherever you get it from whether it's your own body or out of a jab of it, takes longer to work in your body to lower the BG. Many T2s therefore have to take a lot more insulin than your average T1 to have the same effect. eg my total daily dose of both sorts was around 30 units whereas a T2 with IR might have to take a LOT more to do the same job - often well over 100 units a day.
Although the slow and the fast have different jobs to do - the fact is that all insulin wherever it comes from will act on whatever glucose is in your blood at the time wherever it came from and injected insulin cannot differentiate and 'save itself' to just do its own job. It just carries on acting for as long as it happens to work. It can't detect if you are hypo or high, it can't act quicker or slower. If your BG drops to 1.8 it can't turn itself off, if your BG is 20 it can't work a bit quicker.
Whereas I generally have lowish BG (in the 6's ish) and no IR so a very small amount of insulin will send me hypo very quickly - 1 unit reduces my BG by 3.0 within a few minutes - if your mum has high IR and needs a lot more insulin to have any effect she most likely wouldn't notice any difference to her BG whatsoever from 1 unit.
I personally would NEVER take a jab of any sort of insulin without testing first unless there were very extenuating circumstances for it.
I think you ought to ask her why she's drinking the Lucozade, does she just not realise how much sugar (or carbs, does she understand about carbs raising BG?) is in the stuff?
It could be you know that she feels hypo after injecting and that's why she drinks it. because if your BG is used to being too high, when you do reduce it by any means, then you do feel hypo - so say it was 10 and had been that high for quite a while, if you reduced it to 9 then you could feel hypo. But you know that isn't really hypo, it's called a 'false hypo' but feels exatly like a real one! but it won't actually kill you - and so to do it gently you could stay at 9ish for a bit and let your body get used to that before reducing it to 8ish and then 7ish etc etc over a period of time.
Sounds to me as if mum hasn't been educated properly about diabetes or insulin. Which is really really pants.