My view on the basic speed. I think that pure flat out speed over say 60m (creatine phosphate system dominant), while not a bad asset for maybe kicking, is not essential for anything much over 400m. Hence the under 10second hills are normally for sprinters. However, thats not to say that aren't useful in improving power(which will effect contact time) and efficiency. So they can be a good tool. Usually used as an alternative of lifting for distance runners.
However, I think by 'speed' the OP ment more in terms speed endurance or the work of the lactate system and lactic tolerance. Basically 400/1500m pace. Hence asking about an equivalent 400m time. It will correrelate. You improve you 400m time then you have improved a system. This system (an exception is the creatine phosphate) will also be involved when running the 5k. Simply to a lesser extent. Improve your 400m by 1second due to bettering the systems used mainly for the 400m will make you quicker. but as the distances get further away, the overlap in systems mainly used become less and less, thus the 5k wont improve to the same % proportion.
If you were to become weaker in another system due to missing 5kspecific workouts for a more speed based workouts then yes, you will likely not improve. If however all the other systems stay the same but you improve one of them, you will get quicker. I couldn't say by how much though. It may be an unnoticable second, it may be a reasonable 10s.
Having said this, the level your daugther is at now, the training plan I wrote would be fine. Even the short hills on there are still focussing on system used primarily for events way over 400m making them much more 5k specific than 400m specific. The 400m time will improve though, since they are more related to 400m primary systems than the mass aerobic work you have been doing.
Only when you are looking for the last few seconds would you need to start looking as far down as 400m specific work. Or if 400m time truly does become a limiting factor. I read about Horwills (forgive me for spelling. The late english BMC founder?) 4/5 second rule. Take 400m time. add 5seconds to the pace per lap each event you go up. 800, 1500, 3k, 5k. This is the best time you can achieve with the given 400m speed which becomes limiting at this point. If the best time is quicker than the PB, then the PB can still be improved without improving the 400m time, although it gets harder to improve with edurance as you get closer to the limit.
http://www.brianmac.co.uk/frankhorwill.htm
Plugging in 70s for 400m gives a best 5k of 18 45.
66/67s gives low 18s which would make 18 30 much easier.
I've always found this a reliable rule. Few men go much under this 4s, few women go under 5s.
Looking at this evidence, I'd conclude that 400m time will eventually have an effect. The hills and partly VO2 will improve this. If you really hit the barrier, 15s hills, 150m-200m reps with long recovery may need to be factored in. I'd suggest not this year though. That 4 will come down.