Yes, they can, because Keepers have browns in their palette of skin colors. Seekers only have browns; a wider range, yes, but only browns. Keepers have blues, grays and browns.
That's the entire point, that Keepers can have tanned and brown skin if they wish. Do they have a lower variety with cooler colors compared to Seekers? Yes, but they also have wider color choices overall. If Keepers had even more brown color variety, then there would be no point in the Seeker's skin tone options, as it's, again, limited to different shades of brown.
Your initial comment alluded to how Limsa catgirls are all Seekers because they can be tanned but the truth is that you can be tanned as a Keeper too, and you literally replied to a Keeper with dark brown skin.
So yes, Keepers can look like a Seeker: they can have tanned and brown skin, even if their choices are lower in this specific color range. But they also have other choices like blue or gray whereas Seekers have brown only. A Seeker cannot even try to get a look similar to a stereotypical Keeper.
To provide another example, just look at the image below showing a tanned male Keeper:
As aceeko said in post #12, that would make Seekers pointless besides lore, as there wouldn't be much distinguishing them besides the more variety of browns Seekers have.
Please check the OP and post #6 where I outline the differences between each clan.
Eyes are the main feature that distinguishes them due to their diurnal and nocturnal habits, but there's also others like skin tone options, distribution of racial tattoos, and finally the longer fangs for the Keepers.
The entire point of this suggestion is just to provide an extra option for Seekers that doesn't even have to be a default but something you'd have to actively choose in the character creation menu if SE implements it right.
There's been plenty of threads and posts in the past asking for the option of fangs for both clans so this isn't even anything new. In fact, many of these posts are tied to a bigger desire from the player base to have the character creation overhauled and expanded, yet it has not been updated at all or with very minor additions like the new beard option for hyurs as a face type... so while this goes a bit beyond the suggestion laid out in this thread, it's high time SE updated the character creation menu.
You can find the discussions I mentioned about fangs for both clans as well as character creation expansion below:
https://forum.square-enix.com/ffxiv/...gs#post6185901
https://forum.square-enix.com/ffxiv/...racter-creator!
https://forum.square-enix.com/ffxiv/...gs#post5466897
https://forum.square-enix.com/ffxiv/...gs#post6118815
https://forum.square-enix.com/ffxiv/...=1#post5186735
https://forum.square-enix.com/ffxiv/...=1#post3707943