Depends what government you're talking about.
Take the Japanese government - they're, as a whole, very clued up in terms of technology. A lot of technological systems there are pretty ground breaking, from the trains that are never, ever late to the systems which held up most of Tokyo despite the magnitude 9 earthquake. I don't usually rush to congratulate any government but in terms of technology, they are in my mind very good. So should they have an involvement in the computer / electronic industry? Sure, I think they do a great job.
Now take the UK government. Oh dear. We have an IT syllabus that exclusively teaches the use of things people never, ever use in the real world (Access anyone?) a rail network that was privatised and has been getting worse ever since, only just thinking about upgrading to IE7 when the rest of us are on version 9 or running different browsers altogether, laws that are being bankrolled by record companies who can simply brainwash the MPs with any crap they choose, almost a complete ignorance of the broadband network until recently, STILL a complete ignorance of IPv6 despite the fact we've basically run out of IPv4 addresses, confusion over basic terminology from "experts" in recent reports... need I go on? The answer to them is a definite no.
So all in all it depends - if a government knows what they're on about and has the potential to make some great changes then yes. If they're just a bunch of layabouts with no interest or clue about technology at all, then definitely not.