Normalmente sim.
As várias regras da manobra de agarrar referem-se repetidamente se você está ou não lutando, e não quem agarrou quem:
If you succeed, you and your target are now grappling [...]
While you’re grappling, [...]
[...] while grappling
Talvez mais revelador:
When you are grappling (regardless of who started the grapple), [...]
Existem exceções, no entanto. O Grab melhorado , por exemplo, tem o seguinte:
The creature has the option to [...] simply use the part of its body it used in the improved grab to hold the opponent. If it chooses to do [this], it takes a −20 penalty on grapple checks, but is not considered grappled itself; the creature does not lose its Dexterity bonus to AC, still threatens an area, and can use its remaining attacks against other opponents.