I think it would really depend on how I put it together, honestly. If I put the single wheel at the back, as with one of the images above, and made sure that the trailer were mounted in such a way that I could not throw off the CG too much to either side, I suppose it wouldn't make the trike unstable at all.
However, if I could keep all the weight centered so that the tongue was neutral, it wouldn't feel like I was pulling a trailer at all (except the added weight, obviously). This is how I try to load larger trailers, as well, so that the tongue is mostly neutral, or under very little load. Never negative load on the tongue, though.
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