New reports do get pulled prior to closing and do impact when and if you close. And even small changes in those new credit reports could wreak havoc on closings. Fannie Mae has yet another updated policy notification about what is done if the lender obtains a new credit report and discovers additional debt.
Don’t close credit cards that have established a history for you; if you close the cards you are shutting the door on the history you created.
The only time you want to close a credit card is in extreme circumstances like on a joint account, post-divorce.