Yes - do a PPL first, for all the reasons B2N2 and rudestuff say.
I did my CPL writtens (slightly less study than an ATPL, but not by much) in my own time whilst working. It was very laborious, time consuming, and required a lot of discipline. But it is possible.
I didn't take time off and crack the CPL in one hit - and wish I had. Stringing it out probably added 10 hours to the bill, which at ~£300/hr for CPL training was extremely non-trivial.