I think sometimes yes, sometimes no. With the parent analogy, a parent can allow a child to get dirty by turning away as the child heads for the mud. However, if a parent does the same thing when he sees his child headed for the bathtub with a plugged-in hairdryer, then he is arrested for causing child endangerment.
But remember that we as parents are tasked to preserve the child's life on earth (typically and for the purposes of the analogy, -- there are extreme instances when we ourselves should prefer a death of our child to his perdition, see e.g. the martyrdom of the Maccabees). God's love does not stop after we experience physical death, so when God allows a death of an innocent, that death brings him closer to God and his suffering has redemptive value for the sufferer or even for the sins of others. This is that suffering of which St. Paul speaks (Col 1:24) as compounded with the suffering of Christ.
So the abandonment of an innocent to suffering and physical death, that Christ himself experienced on the cross is analogous to a parent allowing a child to play in the mud and scrape a knee. Defiance of God that condemns a hardened sinner to Hell is analogous of a child fighting off the protective parent when heading for electrocution. There is never an analogy of God watching us indifferently as we set out toward perdition, like a neglectful parent would.
Catholics pray for a good death, and beleive that suffering leading to death in a state of grace is a gift from God. But such death is a good, not an evil.