I will give you a method based on constraints and dealing with multiple bodies but for the best accuracy to your exact question, could you define the term “wrap”; a single body that has taken the shape of the main body eg. A label wrapped around a complex container. or are you looking to extrude a flat shape and then make it contour around a shape…? for this I would say that would be nearly impossible with direct modelling and even very difficult for parametric modelling.
Now onto a possible solution…
#1
I understand you do not want to do this with sketches or projects so instead we will use the shell tool this allows us to overcome 1 of the problems for a single body, a better example than I can write out can be found in this short video.
#2 For multiple bodies
Using the align tool will only take your existing bodies and move them to a selected place so that doesn’t help you as much…
trying to use the select and transform tool might work for simple parts but will kind of distort the part.
Then we will have to sadly make a new sketch but use the constraints of the original body we are trying to wrap around the form of the complex body simulating the interaction of parts as they would move around the form and then create new parts and probably use off set sketch tool and match the thickness of the original form we are trying to wrap.
This request is asking a lot of the software to solve a lot of the geometry for you and a little backward thinking when creating a model as this seems to be trying to create a simulation of a non-solid non-using solid bodies.
If we change the thought process from “take part or parts → wrap around the body” to “build the part or parts around the body → build the flat model of body or multiple parts using this wrapped part as reference” it will make the design process more streamlined and possible to achieve your result.
of course, with 3D modelling there are 100 ways to do the same thing and this is only 2 ways but, I hope this helps you with future projects in the future.
Cheers and happy modeling!!