What specific wallpaper have you already bought, or are you still choosing? That matters because the answer depends on it.
Universal adhesive is really a compromise, like people have mentioned here already. But here's the catch: it works fine on medium-weight wallpaper, but at either end of the spectrum it can let you down. If you've got heavy vinyl or textured wallpaper, universal might not hold strongly enough, especially if your place is on the humid side. If it's thin paper, there's a risk the adhesive will soak in unevenly and you'll get bubbles. That's why specialized adhesives exist: they account for material density and how much moisture it can absorb.
Practical tip: before you buy, check the wallpaper roll - there's a recommended adhesive listed there. It's not a marketing gimmick, it's genuinely based on testing. If the wallpaper is universal (that's usually what it'll say on the package), then yeah, one adhesive for the whole room will work. But if you've got, say, fleece-backed plus vinyl in different areas, it's better to grab two adhesives - cheaper than re-hanging sections a week later.
One more life hack: mixing different adhesives straight in the bucket is cheaper than making extra trips to the store. Buy both at once if you're unsure - one adhesive isn't expensive, and having to redo it costs time and stress.