No.
There are 2 Holy Days of Obligation.
The first is Immaculate Conception. That’s one obligation to attend one Mass.
The second is the 2nd Sunday of Advent. That’s one obligation to attend one Mass.
Attending only one Mass in an attempt to fulfill two separate obligations doesn’t work.
First, a little background (ie liturgical law).
In the Universal Norms on the Liturgical Year and the Calendar
The Sundays of Advent are assigned rank #2
The Solemnity of the Immaculate Conception is ranked #3
When a single calendar day includes 2 celebrations, the one with the higher rank (ie lower number) always takes precedence.
In this case, this year, it’s not the same calendar day, however, Saturday evening is the “overlapping” time. The 2nd Sunday of Advent begins on Saturday evening.
Normally, the feast of the Immaculate Conception would continue until midnight—however because the next day (ie 2nd Sunday of Advent) is a higher ranking celebration, the Sunday takes precedence and the liturgical day of the Imm. Conception ends at the time of Evening Prayer I for Sunday (ie. Saturday at 4 PM).
That’s a long way of saying that the answer to your question is:
Yes–attending Mass on Saturday evening fulfills the Sunday obligation, because at 6 PM, the 2nd Sunday of Advent has begun and the Solemnity of the Immaculate Conception has ended.
The pastor should (and hopefully will) schedule the proper Mass for that time/day—6 PM Saturday is the Sunday Mass.