It's ambiguous, and therefore up to the DM
The answer isn't covered in the rules
Other answers here argue for a rules-as-written answer one way or another. I don't think there is one. The rules just aren't clear. For instance, we don't really know what "merged" means, in this context. Does a merged object "exist"? Does a merged object somehow in some sense just not exist while merged? Not only do the rules not say in this specific case, but these concepts in general just aren't covered in the rules, and dictionary definitions, while at times useful, at other times fail to really fully explain the meanings of such words in a magical world.
You can argue either way
You can argue that a merged object still exists, and can therefore be located, you can as easily argue that a merged object in some sense no longer exists, and so can't be located.
You could also argue that a merged object "has no effect", and so can't be located, or you could argue that being located is not an effect of the object at all, but merely because it exists.
The rules don't say, so the DM needs to decide
The rules of magic just aren't well-defined enough to clearly give us an answer. That's okay, because the designers expect that, and expect the DM to resolve the issue.1
In the end, the DM will need to decide which way to go. There are more or less three choices:
- locate object can detect a merged object
- locate object cannot detect a merged object
- something else
So how to decide?
Does one choice or the other break the game?
I don't think so, but if you as DM think so, then, yeah, that's a pretty valid reason to decide one way or another.
I'm not really seeing deep shenanigans either way; although maybe there's less minor shenanigans by allowing locate object to detect a merged object. I'm looking at you, party of three with a dog, sauntering out of the Royal Museum with the priceless Crown of the Queen-mage merged into your druid, as the guards locate object in all directions.
Does one choice or another favor the PCs?
I tend to want to make things work better for the PCs, when there's a choice, even if it means upping the difficulty of the adventure in some other way. Maybe one interpretation or another favors your PCs. I'm looking at you, party of three with a dog, sauntering out of the Royal Museum with the priceless Crown of the Queen-mage merged into your druid, as the guards locate object in all directions.
Do you have a personal preference?
Does one interpretation or the other just make more sense to you? All other things being equal, that's a pretty good way to go.
My recommendation
I lean toward locate object can detect merged objects. This subjectively feels more reasonable to me, and maybe a little less gimicky. Also, it makes locate object slightly more useful, and although I've heard of it being particularly useful in other games, I've never been in a game where someone actually had it memorized, and then used it effectively, except in very niche circumstances.
Oh, that "something else"
Completely unsupported in the rules, but you could consider something slightly less binary than it works or it doesn't. Maybe:
- locate object works, but the distance is halved
- locate object can't detect merged mundane items, but can detect merged magic items
- the issue is resolved by some sort of ability contest, for instance, the wisdom of the druid versus the spellcasting ability of the caster of locate object
Whatever you choose, if you find out it doesn't work in your game, you can certainly reverse your previous ruling and rule a different way.
1 We all know this but, it's worth explicitly remembering that the designers expect that there are gaps the rules don't cover. It's sometimes useful to build logic constructs based on the rules, but if those constructs don't feel like they're serving us, it's also explicitly okay for the DM to make a ruling and move on. This quote from Xanathar's is probably familiar:
The DM is key. Many unexpected events can occur in a D&D campaign, and no set of rules could reasonably account for every contingency. If the rules tried to do so, the game would become a slog. An alternative would be for the rules to severely limit what characters can do, which would be contrary to the open-endedness of D&D. Here’s the path the game takes: it lays a foundation of rules that a DM can build on, and it embraces the DM’s role as the bridge between the things the rules address and the things they don’t.