No. If you can drag lair traits to you, you can eventually merge with the Horror, via. primordial pathways and gain a massive stat buff. Here I'll just copy paste the book.
Beast’s Horror has a much larger, more potent
presence within the Primordial Dream than others. The Horror uses the highest of the Beast’s Strength, Presence, or Intelligence as Power; Dexterity, Manipulation, or Wits as Finesse; and Stamina, Composure, or Resolve
In addition, the player gains a pool of points equal to (Lair x 2) to distribute between Power, Finesse, Resistance, and Size as she sees fit.
Horrors have access to the Beast’s Atavisms (but not Nightmares, which require more finesse than the Horror can manage). The Horror can use any aspect of an Atavism — normal, low Satiety, or Satiety expenditure,
though the latter still requires spending Satiety.
Also, the Beast counts as always being in a Lair-resonant location when acting inside the Lair. When a Beast enters her own Lair (or a Lair connected to it as a Brood Lair) via a Primordial Pathway, she immediately merges with her Horror. She likewise instantly separates if she uses a Pathway to leave. The
Horror itself only leaves the Lair (barring Inheritance; see p. 234) when Starving or Ravenous, and no power can force it to do so in other circumstances. When merged with the Horror, the Beast cannot choose to use the low Satiety version of her Atavisms unless her
Satiety rating is actually low.
The balance to the Horror’s great power is its vulnerability; unlike dream-walking prey, it is wholly present in the Lair. If the Horror is killed, it and its Beast actually die.