Short answer, yes.
Live chat is a great sales and customer service tool for fashion designers and retailers. It allows customers to have their questions asked and answered quickly so they can get on with the purchase without waiting to hear back via email.
Imagine going into a retail store, browsing around, asking the retail assistant if the top you're looking at comes in any other colours, then having to wait 2 days to hear back. That's basically what email does to the purchase experience. You're ready to buy, but want a few quick questions answered, and now you have to wait a day or so to hear back.
Live chat does require energy to be effective. There's no point slapping it on the site, and only having someone online for an hour a day. You need to have someone monitoring it throughout the day, answering the questions.
Just like everything online, it's completely trackable and measurable. After a week you'll be able to see the conversion rate of people who've engaged in chat, and in most cases, this will be pretty damn high.
There are a range of live chat modules out there including Zopim and Zendesk. Most of them do a great job, with a range of reporting and customisation options.
One of the biggest considerations we have in fashion is 'does live chat fit with the brand?'. Now we're never going to put up the module with an image of a lady wearing a headset and big 'click hear to chat to an agent', but in saying that, typical customisation options are limited. We tend to suggest change the wording to be more like 'chat with a stylist' and really push that it is actually a real person who understands the brand and can help you with what you're looking for.
Summary line, it's worth a try if you can make it work with your brand's aesthetic and resource. It helps customers get the answers they need to convert to sale.