No, nor did they compete in the SANFL (bar Port Adelaide) or the WAFL.
Here is the difference:
7 current AFL clubs competed in the VFA pre-1897. (9 if you want to include Sydney as South Melbourne and Brisbane Lions as Fitzroy.)
1 current AFL club competed in the SANFL.
0 current AFL clubs competed in the WAFL.
Futhermore:
All of the 8 VFL foundation teams had previously participated in the VFA. By 1908, all 10 VFL clubs had participated in the VFA pre-1897. By 1925, 11 of 12 VFL clubs had. (Guess who hadn't...

)
This shows that while the VFL was not a direct continuation of the VFA, there was very little difference. The AFL still has very strong links back to the VFA, and in repetitive dick-measuring conversations, we can certainly claim our VFA flags have more relevance than any SANFL flags.