"Hyperfocused" - I will never forget the first time I was called that. I was insulted as I took it instantly as an insult. Perhaps it was the context, perhaps the messenger, perhaps the ignorance in its definition, maybe - as is often the case - the truth behind it. This was some time ago and I haven't really thought TOO much about it since then.
Recently that word has come up again so I decided to look it up - according to Webster what does this mean? It is not in Webster...so does it not exist? I tend to live by the "if it is not in the dictionary it is not a word" philosophy. So I decided to use what brain I feel like I have left these days - I do have an 11 week old - and I used Webster to look up "hyper" - adjective - "high-strung, excitable, extremely active". Then I looked up "focused" - the intransitive verb form is defined as "to concentrate attention or effort." So if I now use my math skills (not so brain fried after all) and add these words together, I can assume hyperfocused means "extreme in actively concentrating attention or effort".
I would say "yes, I can be hyperfocused when something is important enough to me". I have also decided that, unless I am "hyperfocused" on something bad, being hyperfocused is not a bad thing, rather a good thing when I am actively concentrating my attention and effort on something good, important, valuable, etc.