No, it would not be correct even by a stretch. Just because there is some superficial similarity, or just because plots of profit function and Laffer curve resemble each other that does not mean they are special cases of each other. For example, the cosmic web structure looks like structure of neurons in our brains, that does not mean our brains are special cases of cosmic web.
- In economics government is traditionally not considered having profit function. Government has its own social welfare function, similarly as individuals have utility function not profit function. We usually talk about profit functions only in context of firms (e.g. see Varian Microeconomic Analysis or MWG Microeconomic Theory). Taxonomy and semantics aside, while there are some parallels between these concepts we often impose different assumptions on properties, shapes or behavior of these functions so they are not really special cases of each other, even if some undergraduate social-welfare/utility/profit maximizations problems might superficially look very similar.
- Even if we would ignore 1. Laffer curve gives you relationship between tax revenue and tax rate. That is not even superficially related to profit, since profit is by definition revenue minus cost ($\pi = PQ-C(Q)$). A more close analogue to Laffer curve, would be the relationship between price and revenue, but even here you have to squint your eyes and force the analogy. Firms do not set prices as shares of your income. Even if they did, firm-customer relationship is fundamentally different from taxpayer-government one. So even though there you could at least find some parallels it would not be possible to defend argument that they are special cases of each other.