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Probably not. Barclays has been known to close an account after it's been opened if the person opens a bunch of accounts afterwards. Chase also does this on occasion. Since you are PIF, keeping the balances low and aren't carrying high balances I wouldn't worry about it, especially since you are planning to garden for a bit.
Different lenders view the amount of new accounts on your report different ways. If you are set on those cards, it may be better to just app for the rest of them now rather than wait, as the "new accounts" likely haven't shown up yet. When doing additional apps with the other lenders, they'll see your inquiries of course, but not the accounts. Seeing only inquiries isn't as "bad" as seeing inquiries and new accounts. Also the inquiries likely are spread across bureaus, where the new accounts will be seen regardless of which one of your reports is pulled.
Also, what specific cards are you looking to take on? You mentioned things like Amex, Chase, Citi, etc. but didn't mention the actual CC product you were interested in. To me, that sounds like you aren't necessarily going after cards, but moreso lenders, possibly trying to get "in" with them. You don't want cards that "you'll use" as you put it... you want cards that you'll use frequently because they provide you with worthwhile benefits based on what you spend. If you're getting a card that you may only use once a month, chances are you aren't getting it for the right reason. Just something to think about and consider here, as I of course do not know what your overall intentions are.
Agree completely with @Adkins and @Anonymous. As long as you don't follow up all of the new accounts with lots of new balances as well, and cool your heels on the apps for a while you should be okay.
Its OK to have cashback cards but analyse your spend for the year and use the card thet will get you the most back then. Having 10 Cashback cards will dilute your cash back(unless) you can spend $1000's on each card or at least hit the max with discover in its rotating categories and your BCE with the number to get a nice amount of cash back each year rom groceries.