Do for sale boards fulfil any useful purpose?

Very much so. In fact, even in the internet age, agents’ boards are still generally acknowledged to be one of the most effective marketing tools in the estate agent’s locker. People really do notice them. What’s more, enquiries that result from someone seeing a board outside your home are often likely to be more valuable that those received via the internet, or from newspaper advertising, since they imply that the would-be buyers have already seen the property and like what they saw. By definition, it also means that they like the location. So, if the price is right, such enquiries will normally turn into viewings.
In the case of vacant properties, boards can also act as a useful deterrent to sneak thieves, squatters and the like, since they will never know when an agent might turn up for a viewing.
Ironically, the most common objection to having an agent’s board outside a property is that the homeowner doesn’t want his or her neighbours to know they are selling. Bizarre, when you think about it. For one thing, the neighbours would have to be pretty slow on the uptake not to notice agents turning up to value the place – often in branded vehicles – or walking around taking measurements and photographs. Then there’s the succession of complete strangers wandering about, very obviously checking the property out - as often as not while clutching copies of the particulars. Not forgetting, of course, the agent’s press ads and window cards…
All in all, trying to keep the sale a secret is something of a tall order. But in any case, why on earth would you want to? After all, you’re trying to sell the place, aren’t you? And particularly in this kind of market, you need all the exposure you can get. Indeed, your neighbours may well know someone who would love to move into the area!
So, in short, I would strongly advise you to have a board. Even if it’s not one of ours!