Short answer. Yes, it can. Failure of the appellant to pay the docket and other lawful fees within the prescribed period is one of the express grounds on which the Court of Appeals may dismiss an appeal, and it may do so on its own motion, without waiting for the appellee to complain.
What the law says
(c) Failure of the appellant to pay the docket and other lawful fees as provided in section 5 of Rule 40 and section 4 of Rule 41
Rule 50, Section 1 — Grounds for dismissal of appeal. Read the full provision →
Non-payment is a listed ground, not an oversight the court must excuse
The rule sets out the grounds on which an appeal may be dismissed, and non-payment of fees is one of them in its own right: failure of the appellant to pay the docket and other lawful fees as provided in the rules governing appeals from the lower courts. It sits alongside failure to file the notice of appeal on time and failure to file a brief. The point is that the fee is treated as part of perfecting the appeal, not as an administrative detail that follows behind it.
The court can act on its own
The opening words of the provision matter as much as the list. An appeal may be dismissed by the Court of Appeals on its own motion or on that of the appellee. So there is no safety in the other side staying quiet: the court may raise the defect itself. Nor does the rule build in a notice-and-cure step for this ground. That is a real difference from grounds where the rule expressly gives the appellant a period fixed by the court to put something right.
May, not must
The rule says an appeal may be dismissed. It is a power, not an automatic consequence, and courts do have room to decide that dismissal is disproportionate on the facts. But that discretion is exercised on the strength of the explanation offered, and it is not something to rely on in advance. If the payment was late, the honest course is to pay in full at once and put the reason for the delay before the court in writing rather than hoping the lapse is not noticed.
What to check right away
Confirm the exact date of payment against the last day of the period to appeal, and keep the official receipt. Check the amount as well as the date — a shortfall can be as much a failure to pay as paying nothing. If the appeal was taken from a first-level court, the fee is paid in the court that rendered the judgment, and the record should show that clearly. Fixing an incomplete payment before anyone moves to dismiss is far easier than defending it afterwards.