IME yes absolutely! It's not a secret that you can calculate to work so many hours/earn so much to be able to get the most out of the benefits system, especially as a single parent and/or lower earner.
Quite a few people I know, just stating fact women who are single mothers or in a relationship with a partner claiming PIP do indeed ensure they work enough to meet the ETA I think it's called. When offered the chance to work overtime or get a promotion involving more responsibility and hours, it's looked at with horror as this would impact upon payments to top up wages, rent allowances etc.
So many factual examples I could give but I will just outline one, an in law. Jade has 3 kids to 3 different dads, the relationships haven't worked out so is a SP. DC are 15, 12 and 8. She was on benefits until getting pregnant with first at age 19, then subsequently for the next two as they were young. Finally had to get a job, knew a minimum of 16 hours would be enough so got one but called in sick so much she got sacked. So, back on to full benefits and looking for work. Got her next job, which was too stressful as had to be at work for 10am 4 times a week, took too much time off, sacked again. Cycle repeats itself.
It may seem reading this that Jade had issues, couldn't cope, but no. Her parents looked after her DC, they lived there, practically brought them up during their first few years as she was out partying, taking drugs and sleeping all day.
As they got a bit older she took on a bit responsibility and had them stay over at her 4 bedroom home which she insisted was needed due to special needs, with no evidence or even any effort to diagnose, just ranting. Only when convenient for her though when she wasn't having parties or picked up a new bloke.
When the time came that she had to work, she went through the motions, expressed how hard life was as a SP with 3 DC to employers and so they were understanding that she needed to take time off because they were ill: reality GPs were taking them to nursery/school and she had just gone to bed.
Also, the dads were paying maintenance, which she insisted cash only, and involved in DC's lives so looking after them in addition to GPs.
Basically Jade had more than enough money to play the system as she had, I quote, over £1400 pm given by dads, UC, parents for childcare. So working was a case of yeah I'll do it but then I won't, still getting all the top ups for those few months barely there.
As I said, this is just one example of people I know, there are others far worse your toes will curl!
Unless you actually know anyone who deliberately calculates, you have NO idea.