Yes they can. This isn't just child support - this is unpaid child support.
Yes, they can - and then you'd have to prove that the funds were yours, and not his.
You ideally need to keep your finances separate until his child support obligation is paid off.
It's more than this....CSED has every legal right to that money, because the NCP has every legal right to that money.
As long as his name is on the account, he has access to the funds. If he has legal access to the funds, so does CSED, and it doens't matter where the came from (as long as it wasn't traceable back to a needs based PA program, SSI, a minor child's earnings or other exempt source), they can and will levy those funds to pay his child support obligation.
If you marry/life with/hook up with somone with unpaid child support--
KEEP YOUR MONEY SEPARATE.