On its own, probably not - but it's an easy matter to split a larger sum, then spend a little time depositing it piecemeal over days or weeks, if doing so will keep you under the radar.
Eh... kind of. There are laws in place that send up red flags if you deposit more than $10,000.00 in cash in a single day. So, doing as you suggest, and making smaller deposits would seem ideal, but banks have ways of noticing those patterns. Banks use computer algorithms that can notice particular depositing behaviors. In fact, depositing small amounts, as you suggest, may actually make it easier to get noticed. Consequently, if banks were actually interested in catching people who were laundering money, they would let them make deposits. The algorithms can't notice depositing behavior if there are no deposits being made. So the Chase policy to not allow people who don't have an account deposit money isn't going to prevent or help catch money laundering.
You also have to consider the amount of time it would take to launder a large amount of money. Think about it - how long would it take you to deposit $5,000.00 if you were making small deposits? How small would you make them? Would you vary the amount deposited each day? Would you vary the bank branch which you deposit the money in each day? That's going to take a lot of time and effort just to launder $5,000.00. Now imagine how much time and effort it would take to do the same for $100,000.00 or $1,000,000.00.
No, if you're going to launder money, you're going to do it a different way, unless you're keen on getting caught. Now, in this particular instance, we are talking about a personal bank account owned by Sabrina's friend. If you are going to launder money, you're not going to use a personal account. A business account is much better.
There are several ways you can launder money, none of which would be stopped by this policy that Chase has decided to implement in order to cause aggravation. As Janx mentioned, money businesses are a good way to go. You can buy services from a legit business. Businesses that accept a lot of cash are ideal. The Breaking Bad idea of a laundry place is a pretty terrible idea. You are limited in how much you can make look legit. I mean seriously, how much money do coin laundry places make? No, if you want to go this route, you would be best served with going with a business that can bring in a lot of cash when run legitimately. A bar, club, or strip club would be ideal. There is a lot of cash exchanged in places like that. This will require that you make up invoices for products "sold." There will be dirty money mixed in with clean money. This money is then deposited into a business account, and because it is a business that makes a good amount of money, large sums of cash being deposited won't send up red flags automatically.
You can also go with using foreign banks to do the dirty work for you. I'm sure you've seen movies where the criminal has some money in the Cayman Islands. Well, it's pretty accurate. I don't know if it is still the same, but you can just open up a bank account in one of these offshore banks, and transfer money from there to a U.S., or any other country, bank. There are a lot of countries where banking laws are very lose. They don't care how you got the money. They just want to have it in their bank. Yes, you can still get caught, but again, Chase's policy isn't going to stop it. Hell, it won't even detect it.
You could also go the shell company route. You can create a shell company and deposit money into it's accounts for services or products that are never actually provided. You have to keep invoices, much as if you funneled your money through a legit business, like a strip club, but you don't actually have to provide anything. In fact, you could have a legit business that deals with a shell company you or someone else has created, and have the shell company pay for services to your legit company. Again, Chase's policy wouldn't stop this method either.
If I were going to launder money, which I'm not, I'd go with a mix of the legit business, shell company, and offshore bank. You can create many layers, so that it is far more difficult for a bank or government agency to notice any suspicious activity. Preventing someone that doesn't have an account isn't going to prevent money laundering. Money laundering is a far more sophisticated crime that requires a bit of know-how. To be successful in it, you need to be intelligent and have an understanding of banking laws. The best guys tend to be accountants and lawyers. they know the ins-and-outs of the financial system.
Note: Doing an of the preceding is illegal. Money laundering is a crime, and I am by no way meaning this post to be an instructional post on how to launder money, nor am I condoning it or encouraging anyone to try it. If anyone is stupid enough to try to do any of the things that I have mentioned, and you get caught, remember... Snitches get stitches. All joking aside, seriously, don't try this at home. You'll most likely end up in jail and become someone's girlfriend.