The best I can say is no but yes.
Strictly speaking, the answer is no. Your gear has a set of stats and an upgrade slot. These stats don't change.
But it's also kinda yes, because it's not much of a problem.
You have complete freedom to transmute your gear in GW2. So you CAN keep the same look you want forever. It might get somewhat expensive over time, but to be fair so does buying mods. The transmutation stones for levels 1-79 are easy enough to come buy in game by doing your daily achievement and completing maps. The level 80 ones are much rarer, but you can still find them. And exchange rates for gold to jewels (RMT currency) are so favorable right now that even level capped you're looking at like 5-6G to transmute a whole set. Now that's not cheap, but it's definitely not super expensive either.
More importantly, the actual stats on your gear aren't THAT important. That's not to say they're irrelevant, but what really matters is the upgrade slot. These are essentially where the really interesting aspects of your gear come from, like set bonuses. When you use a transmutation stone, you choose which upgrade to keep (if there are two involved), so the real essence of your item is always transferred with the skin if you want it.
Finally, because GW2 gives you complete freedom to dye your gear (well, each item has 2-3 dye "slots" that correlate to parts of it), you'd be surprised what you can do with some skins that don't seem attractive at first. It's not going to salvage something you hate, of course, but the colors right and outfits really do come out seeming completely different, depending on how you downplay or highlight components.
So yeah, it's really not hard to keep your look in GW2. If you are dead set against paying real money, it does get harder. But as long as you aren't transmuting your gear nonstop, it's nothing a level capped player shouldn't be able to realistically handle purely through in-game currency (especially once supplemented with random quest rewards and Black Lion Chests, which contain items from the RMT shop but are found in game).
The flip side is that GW2 is 100% free with purchase. There are NO content restrictions like in other F2P games. Real money is used for boosters (items that give temporary buffs to things like magic find chance, experience gain, karma gain, etc.), aesthetic items (skins, dyes), and other upgrades (additional bag slots, additional bank slots, additional character slots). The only thing like content you have to pay for is the tournament (essentially, WoW's arenas), and you can get those tickets with gold if you want. So even if you DO feel like using real money now and then, you'll probably pay less than you would even in other F2P games.
TL;DR: No, you can't mod items. But you can transmute the skin onto a new one, and the "upgrade" you put in it usually matters more than the actual piece of armor anyway. If you want to keep the same look forever, you can, but it might be annoying if you aren't willing to pay real money.
It'll be close, but Romney has the momentum.