I pretty much agree with flyboy, other than the compatibility between Peco and Atlas.
What you need to know is this, referring only to Code 83 Track. Atlas' version of the Code 83 track is only a revamping of their Code 100 track. In other words, the ONLY difference between the Atlas Code 83 and Atlas Code 100 track is the height of the rails.
What that means is this - the 'base' or bottom of the Atlas Code 83 track is actually Code 100 and that is not compatible with true Code 83 track. What that means is you cannot use Atlas Rail Joiners between Atlas and Peco (or any other true Code 83 track) because the 'width' of the joiner is too wide to connect firmly or properly. Conversely, you can't use (for example) Peco code 83 rail joiners as they are will be too narrow to connect with the Atlas. Nor can you use Universal Rail Joiners as they are made to true Code 83 specifications.
As we all know, one of the most critical elements of a layout is the continuity of power throughout the layout, the track work. That power is passed from one section of track to the next via the rail joiners UNLESS you have feeders to each and every section of track on your layout. We also know that the majority of issues with track seems to revolve around the turnouts where, if you are using Insulfrog Turnouts for example, you have no power directly connected to the turnout and are completely reliant upon the rail joiners to provide the power to the turnout.
If you agree with the above, in its entirety or even in part, you have to believe that anything that may result in 'poor' continuity of power to your layout is not a viable option and should not be used if you want reliability, and problem free operation of the layout in terms of power.
Yes, you probably can connect Atlas to Peco BUT, at what potential cost? Is it worth 'jerry rigging' something up for the sake of convenience, or as a temporary resolution? I fail to see how what ever worth you may acquire from doing that is worth the potential issues that may arise in the long run.
The answer, therefore, is a simple one. In order to minimize any potential problems (power and connectivity wise) you need to choose between using Atlas Track or another manufacturer of track be it Peco, Flieschmann or any other maker of Code 83 Track, as each other makers Code 83 track is compatible with each other; where as, Atlas Code 83 Track is only properly and fully compatible with Atlas Code 83 Track.
In conclusion, I too found it necessary (in the beginning) to connect Peco Turnouts to Atlas Track. The result? I ripped out all of the 'new' Atlas Track and replaced it with Peco Track. This decision was undertaken due to compatibility issues AND, the quality of track and turnouts of Peco being superior. The choice is yours, but do not try to mix Atlas with any other maker of Code 83 Track. Pick one or the other - definitely not both.