Yes, and many members do exactly this. Most of the Calixpert programs were designed to be done with minimal fixed equipment, which makes outdoor training a perfectly viable option.
The main thing you need outdoors is a pull-up bar. Most parks and outdoor gym areas have one. For pushing exercises, parallel bars, low bars, or even a sturdy bench can substitute for dip bars. For band-assisted exercises, you can anchor a resistance band to a low bar or post.
Training outdoors has real advantages. Fresh air, natural light, and the change of environment can make sessions more enjoyable. A lot of members find they push harder outside than they do staring at a wall at home.
The one thing to plan for is weather. Cold weather means a longer warm-up before your hands and joints are ready to work. Wet bars require extra grip attention. Neither of these is a reason to skip a session, just something to account for.
If you are unsure whether a specific piece of outdoor equipment works as a substitute for what the program calls for, post a photo in the community and we will confirm it.