Short answer to your question...No. There may be a few that do but its more the exception than the rule.
I had a conversation about this with an active JW friend several weeks ago. The JW mentioned something about the unity and genuine hospitality of the Witnesses so there is not a need to compensate with gifts that don't mean anything.
Even as a JW I gave gift-wrapped presents to friends and family and became known as a giver. Now ask me how many presents I've ever received from a JW? Outside of graduation from elementary school, high school and my going away party when leaving to "serve where the need is greater"...nothing. JW friends would tell me how special they felt when they received a gift from me...guess they never wanted me to feel special.
A couple of years ago, I recommended to my siblings that we choose a day and each present our parents with gifts. They made jokes about celebrating mother's and father's day but at a different time of year but they went along with it. It turned out very nice and my parents were very surprised. But here's the kicker, its so uncommon for JWs to give gifts that my young JW nieces, nephews and cousins had no idea what was going on. They asked why were we giving them gifts? My young nephew turned to his mom and said "But we don't celebrate birthdays and holidays". The concept of receiving gift-wrapped presents or even presents in general were so foreign to them.
I have always, even when I was an active JW, sent my young relatives gifts right after the holidays and have been accused of celebrating Christmas undercover. Ha...simply because I chose to take advantage of the great deals to do something nice for the kids in our family I'm celebrating the holidays?