Short answer. Yes. Section 7 of Rule 120 says a judgment becomes final when the sentence has been partially or totally satisfied or served, as an independent event from waiving your right to appeal in writing. Starting to serve your sentence triggers finality on its own, separate from the other listed grounds.
What the law says
a judgment becomes final after the lapse of the period for perfecting an appeal, or when the sentence has been partially or totally satisfied or served, or when the accused has waived in writing his right to appeal, or has applied for probation
Rule 120, Section 7 — Modification of judgment. Read the full provision →
Why finality of judgment matters here
Before a judgment becomes final, it can generally still be modified or set aside on the accused's motion. Once it becomes final, that window closes, and the judgment is treated as settled for purposes of appeal and enforcement. Section 7 lists the specific events that trigger that shift, which is why identifying exactly when finality occurred matters to whatever you are trying to do next in your case.
Four separate roads to finality
Section 7 lists several distinct events, any one of which makes a judgment of conviction final. A judgment becomes final after the lapse of the period for perfecting an appeal, or when the sentence has been partially or totally satisfied or served, or when the accused has waived in writing his right to appeal, or has applied for probation. Each is joined by or, meaning any single one is enough on its own.
Why serving the sentence is its own trigger
Partial or total satisfaction of the sentence is listed as a distinct ground for finality, separate from the written-waiver ground you are asking about. Because the article treats these as independent events, you do not need to have formally waived your right to appeal in writing for the judgment to become final — beginning to serve the sentence is enough by itself under this clause.
Why the rule is written this way
Accepting and beginning to serve a sentence is conduct inconsistent with still contesting the judgment, which is likely why the rule treats it the same way it treats an explicit written waiver — as a basis for treating the case as settled. The rule does not require a separate, formal declaration on top of that conduct before finality attaches, since the act of serving the sentence already speaks for itself.
What this means for your situation
If you have already started serving your sentence, Section 7's own language points to the judgment being final on that basis alone, regardless of whether you separately signed a written waiver of your right to appeal. The absence of a formal waiver document does not, by itself, keep the case open once service of the sentence has begun, since satisfaction of the sentence is its own independent ground under this section.