Yes they issue check for cuenta corriente, and checks are used for payment for larger transactions and as payment for services rendered etc., they will not be used at supermarket or chain stores or burger outlets. They will be sued for example, for paying for goods bought on pre-approved credit etc. Noone will just accept check form somebody unknown and dispatch goods and maybe never see the goods nor money again.
Having said that, as MpJuly correctly pointed out, here it is easier to use savings account (cuenta de ahorros), banks even issue you a debit card, and you can usually do unlimited transactions (not just 5 per month like in the US). Many (including myself) use it as transactional account, because fees and minimums are lower than on checking account. Basically, in the DR, you get a checking account only if you want to write checks, else you get savings account.
USD denominated checks drawn on US bank take anywhere between 20 to 30 working days to clear, depending on the bank.
