I think it depends on the situation. If we're talking about someone who had a perfectly good job (one which paid a living wage and benefits which they could actually reasonably raise a family on) and quit it because they simply preferred to be a SAHP then no.
But I highly doubt that is the typical situation. Here's an website with statistics that show that women on welfare tend to be have little education and few job skills. Of those who did get off of welfare and maintained employment 41% of their employers reported an absentism problem--and 64% of the time the problem was childcare, 41% of the time it was transportation, and 34% physical health, 8% domestic violence, and 5% mental health.
Of those who were receiving welfare in 1995 and by were employed 1998-99, 65.7% were earning wages that were below the the poverty line and only 58% received health benefits for their family. Of former welfare recipients 46.1% had been unable to pay their mortgage, rent, or utility bills at least one time, 25% worried they might not have enough food to last until their next paycheck, 32.7% skipped meals or cut the size of meals to save money, and 14.6% ran out of food and had no money to buy more.
So it seems obvious from the statistics that what happens to most women when they get off of welfare is that they are still impoverished, they still have no healthcare (or must depend on the govt for it), they often can't pay major bills, they sometimes don't have enough food to feed their children, and chronic problems with child care and transportation tick off their employers. One of my dissertation advisers was recently telling me about sociological work that has found one of the big problems for former welfare recipients in employment is that the great majority of jobs they can get do not allow them ANY contact with their children during their work day--i.e. they cannot call home to make sure the kids got home after school okay, they cannot take a call from the babysitter saying little Suzy broke her arm, etc. (My father actually has this type of job. He gets demerits everytime someone calls for him--whether it is an emergency or not. When his elderly mother kept falling and needing to go to the ER my mom would call him. He eventually told her "Look, unless my mom is dying or in need of surgery you need to stop calling me and handle it on your own. My bosses are NOT happy."

Luckily my mom was a SAHM though, so my brother and I could always get in touch with her. I don't know what a kid does when their one parent or both of their parents work jobs like my dad's? What if the kid forgets their house key? Or they miss the bus at school? Or they break their arm? Guess they have to wait until 5pm.)
Seems to me that the most smartest thing to do is just keep receiving welfare as long as one can. If your choices are--go to work, live in poverty, get no benefits, not have enough for food, have no contact with your children for 8 hours, possibly pay someone else a huge chunk of change to watch your kids OR stay on welfare, live in poverty, get food stamps, and stay home with the kids and watch them for free--it's a no-brainer. And statistically it is clear that for most welfare recipients, those are the choices. If I were in that situation, I wouldn't get a job either.
If we want to change the situation of welfare recipients it seems the first thing is to make it the case that there are actually very high incentives for employment, education, and various kinds of training as well as subsidized childcare and transportation to school/work subsidies. Make employers pay a living wage that one can actually support a family with. Instead of taking benefits away when people begin to work, continuing offering benefits so that working + welfare benefits is a significantly better situation than just welfare benefits. As far as I know, the govt often provides bonuses to companies that higher former welfare recipients; if they are giving bonuses they can also provide oversight. Make it a requirement of these companies that the former welfare recipients be allowed to take and make calls from their children. Require the company to provide health care to the worker and her children. Give extra bonuses if the employer provides low cost childcare onsite.