General,
In short, yes.
In the company I work for we have the 777-200ER and 777-300ER. Because of different engines, divert speeds and policies these two planes have different critical ETP requirements. In fact each plane can have different critical ETP requirements on a single flight.
Both types work on 180 minute EDTO (replacement for ETOPS). EDTO does not take into account depressurisation, but rather engine failure or failure of a significant system. The ETPs however can look at depressurisation.
Typically on the 200ER we will have an ETPD, that is a plan that accounts for a depressurisation. For the parameters that the company has set on this type the depressurisation is typically the most restrictive. On the 300ER however we typically see an ETP1D, which is a combined depressurisation AND an engine failure.
What is important to note is the difference between the EDTO requirement and the information given by the ETPs.
EDTO is for an engine failure or other significant system failure, but not depressurisation. For most operators of the 777 this will be 180 minutes. ETPs are for the situation that the company has decided will be the most critical for their parameters. As such you will see ETPs that exceed 180 minutes (or whatever limit has been imposed). For example an ETPD can show a divert time of greater than 180 minutes. This is because the depressurisation situation is quite different from the engine failure situation. Whereas an engine failure will mean a descent to approximately 20,000', a depressurisation will mean descent to 14,000'. This results in a vastly different TAS, and therefore the depressurised flight can exceed 180 minutes. This is perfectly in line with the rules.
The main thing to know is that we always have the fuel to get to our divert, whether it be on one engine, depressurised, or a combination of both.
Hope that helps.