I'm an attorney and although i don't practice in your state i do practice child protection law.
I can say that where i am yes, if a baby were to test positive for marijuana that could, in of itself, be a basis for removal. However, usually removal is an extreme measure that's only taken if certain other markers are there. The less extreme measure is an order that allows CPS to supervise you, which means unannounced home visits and a promise to say clean, potentially with regular drug screening. I hate to say it but where i am a white lady with a decent job whose baby tests positive for marijuana is far less likely to have her baby removed than a poor black woman with the exact same results on the same test. It's really sad but the system is both racist and classist.
I do not think think they screen for drugs unless there's some other reason to. If you were to admit that you used any drug in the past, then, depending on the care provider, this could be used against you and you may be pressured into testing or have some blood snuck from babe. My advice would therefore be to not reveal your marijuana use to anyone who you're involved with for the birth, even if they say stupid shit like "are you sure" or try to scare you into revealing. As far as you're concerned you're society's ideal of the 100% pure mother.
I don't think it makes sense to have a plan to say yes to tests so as to appear cooperative, because then if you say no to this one test it could raise flags. If anything it might seem more consistent if you said no to most tests as then this would just be one of a long list.
To help set the stage, and to protect yourself, I would have a written document with you (like a birth plan) that states very clearly ahead of time that you do not want any additional tests done on baby other than (whatever you choose). Ask that the document form a part of your medical record and make sure your husband speaks up about it too. Having your husband speak up for you during the birth, and protect your wishes, can go a long way.
If anything does happen, and CPS gets involved, do not say anything to anyone until you speak with a lawyer. I cannot emphasize enough how important that is.
To conclude, i would say that although it's possible that your concerns could come to fruition, i seriously doubt that they would. I know you're first time mom so it's super scary but seriously, this is not a realistic possibility unless you blab about it openly in the hospital. Keep your mouth shut about it, and be assertive about tests in general, and you'll be fine.
As an aside I personally don't think pot use during pregnancy is a big deal, there are woman who take pharmaceuticals that have documented chances of adverse outcomes. The weirdness about pot is mostly emotive and is not science based. Godspeed to you and don't mind the witch hunting idiots that far outnumber us.