Yes you can, but I believe the rule is you can only use half of your part 61 training/flying. Depending on how greedy the school is you can complete your training by completing several lessons at once. So even though you have to complete all the lessons, your first flight could be lessons 1-5 if you demonstrate enough proficiency to move on to lesson 6. Some schools will even do a "placement" flight to decide where you should start in the syllabus.
So really, the only thing you have to decide is will you have to fly more (i.e. spend more) part 141 or part 61. Here is the kicker. If you have 120 hours it makes absolutely no difference. If you have 120 and you go 141, you can use 60 hours towards 190, leaving 130 hours to be flown. If you go part 61 with 120 hours you need 130 hours to reach 250, so its a draw. Either way you'll end up at 250 hours, so what it really comes down to is who is going to charge you more for the airplane!