Short answer. No. Rule 76 states plainly that no newspaper publication shall be made where the petition for probate has been filed by the testator himself — so petitioning to probate your own will while you're alive removes the newspaper publication requirement that would otherwise apply.
What the law says
But no newspaper publication shall be made where the petition for probate has been filed by the testator himself.
Rule 76, Section 3 — Court to appoint time for proving will. Read the full provision →
The general publication rule
Rule 76, Section 3 sets out the ordinary process for probating a will: when a will is delivered to, or a petition for the allowance of a will is filed in, the court having jurisdiction, such court shall fix a time and place for proving the will when all concerned may appear to contest the allowance thereof, and shall cause notice of such time and place to be published three weeks successively, previous to the time appointed, in a newspaper of general circulation in the province. That three-week newspaper notice is the ordinary rule for probate petitions, meant to alert anyone who might wish to contest the will before it is allowed.
The exception for a testator probating his own will
The same section immediately carves out your exact situation: but no newspaper publication shall be made where the petition for probate has been filed by the testator himself. Because you are the testator filing to probate your own will while still alive, this exception removes the newspaper publication step the general rule would otherwise require, sparing you that particular expense and delay in your own probate proceeding.
Why the exception makes sense
Newspaper publication in the general rule exists largely to reach people who might not otherwise know a probate proceeding is happening, so they have a chance to appear and contest it. When the testator himself is the one filing the petition while alive, that underlying concern is far less pressing — the person whose will it is has brought the matter to the court's attention directly, rather than the court needing to reach interested parties on his behalf through a public notice they might never see.
What still happens even without newspaper publication
The exception removes the newspaper publication step specifically — it does not say the court stops fixing a time and place for proving the will. The rest of the process described in Section 3 continues to frame how a probate petition, including one filed by the testator himself, moves forward before the court, right down to the court fixing a time and place where anyone concerned may appear.