Well, no...
We try,  but the variety in email clients is just too large. We know the limitations of many of the email clients, and apply specific fixes where possible to get past 'known issues'.
But you have to keep in mind that Outlook 2003 was developed / released in 2003 (and still has many users...). GMail is filtering all kinds of code needed to make emails look good, and so does Outlook.com.
Mozilla Thunderbird displays most emails very nicely, but more recent versions of Outlook are known to filter certain code also, except when specific fixes have been applied.
And of course a responsive template adapts itself to the max. width of your mobile or tablet. Any email on an iPhone / iPad or an Android device will look different then on any of the desktop email clients. But these adaptions can be controlled to a certain extend, and we will ask for your input on how to shift content around for a mobile browser.
In short, we work around issues as much as possible, and communicate what cannot be done with you, so that you either know what you accept or have a chance to change the parts of your design which cannot be made fully Cross Browser Compatible.
There are technical limitations...