Can a Hamster Kill the Grim Reaper?

I have a question about Life & Death. I don't own it yet. I've made up my mind to buy it, but I haven't decided when. Now, I'm currently playing a legacy challenge. My current generation is pretty straightforward, but I'm concerned about her grandchild (not born yet, but let's call the kid Robin). Here are a few of Robin's generational objectives:

• Reach the top of the Reaper career 
• Die of Rabid Rodent Fever
• Be Reborn 👶

If someone owns both the My First Pet and Life & Death packs, is this achievable? I heard that reaching the top of the Reaper career causes the sim to turn into the Grim Reaper and become immortal. Does this mean that Robin can't be attacked and killed by an angry rat and be reborn as someone with a weird vendetta against tiny pets? 🐀 I hope someone can shed light on this important topic.