Firewall is part of the Operating System. System and Firewall attributes are derived from the Operating System (the last sentence is from the despised Unwired pg48).
The processor limit is based on System attribute. So no, neither System nor Firewall program affect the Response, but all are limited by Response rating.
The logic is simple. No hardware can run at full capacity software that is designed to run on better machine. No software component can be run at the higher rating than the frame.
RL examples.
You can run win xp on 386, just don't expect it to work at the speed of running it on laptop from 2002. On the other hand there is no noticable performance upgrade on running it on laptop from 2010.
You can open old version attachments of excel in old powerpoint, you can't open newer ones unless you strip them of tags, that old version cannot interpret.
SR examples.
You can run System 6, Firewall 6 Operating System at Response 3. But the effective attributes will be reduced to 3.
You can run Attack 6 program, on System 3, but the effective rating would be reduced to 3.
And the discussed example. You can run Firewall 6 at System 3, but the effective attribute will be reduced to 3. Note that in Core no OS have Firewall higher than System and none of the example runners have links that despite some of them having modifed commlinks violate the rule of
Response >=System>=Firewall,Program ratings