There's always risk of vomiting, part of the benefit of injecting drugs to euthanize yourself in my mind is the idea that once it's in there's nothing anyone can do to get it out. Resuscitation would become damage control, whereas if you swallowed it they could potentially pump your stomach (if they respond soon enough), give you charcoal, or other things to neutralize the substance/prevent absorption. You have to consider that there's different mechanisms for vomiting, too. For example. certain medications (or formulations) can irritate the stomach. NSAIDs (non-steroidal anti-inflammatory drugs), for example, can cause stomach ulcers and so when people swallow a lot of tylenol or advil, for this reason you vomit because your stomach becomes irritated.
I'm honestly really not sure if I can answer this, because almost all metrics of fentanyl lethal dosage are for IV use. Fentanyl is not a drug which is generally taken orally. That being said, you should consider that going through the digestive system you will need more considering it takes much longer to absorb compared to IV, and not 100% of what you take will be absorbed. It's not like if you were to inject it and you would near-instantly get a huge hit of it. I still doubt that you would need such a large amount, to the point that your stomach would become irritated to the extent of vomiting. However, you want to consider for most people suicide can be an anxious or worrisome process and your mindset may cause or worsen nausea and vomiting.
I doubt you would vomit, but, it would also be hard to know how much you need as this isn't necessarily a well-researched way of taking fentanyl, even in the wider medical community beyond CTBers. I've never heard of people taking fentanyl orally, it's really only used in surgeries or emergency pain management - meaning it needs to be strong and have a fast effect. For this reason clinicians usually give it IV.