This question is one I have heard more often than just about any other in my 40-plus years of law practice. In most situations, the answer is a very definite NO. This kind of question most often has come up in situations where a client owes a large amount of money, a bill collector is demanding a correspondingly large amount of payment, and the client feels that by sending $10 or $20 each month, that should stall the bill collector from being able to file a Court case. Ordinarily, the only time making a regular payment will prevent the other side from having rights to take you to Court will be a situation where you have an agreement to make a regular payment in that amount.
While it is true that a creditor must credit your account with whatever payments it has accepted from you, it is also true that in many situations the creditor is not required to accept a small payment, and the fact that you tender a small payment does very little to mitigate the situation. If you have a question about this sort of thing, it is appropriate to raise it with your lawyer.