You could do it. But buying up a bunch of infrastructure and business tends to attract the attention of power rivals, and on many fronts.
You don’t exactly have a title to anything except the pieces you buy, so you’d have to declare yourself some title of “Lord Protector” or something, and how do the real nobles from around Amphail feel about that?
Especially the nobles with a stronger pre-existing claim, according to the byzantine claim accounting system of noblility, are going to look at you and slot you into their view of local power dynamics. To each of them, you’ll be seem as one or more of “potential enemy”, “potential ally”, “potential useful tool”, or “existential threat to be destroyed at all costs”.
Individual local merchants and business people are going to either see this sudden takeover as hostile or benevolent or a mix, depending on how they perceive you personally, how your power moves impact their wealth and business.
Anyone who holds power by force of arms is going to look at that outpouring of wealth and wonder how you fit in. Will you be a wealthy benefactor, can you hold what you own against force, or are you ripe for having your new toys taken away? Can you actually protect Amphail, or are you just a bag of money for the taking?
What about the underside elements of the city? Will they see you as a threat to their operations and power, a mark to steal from or bully, or a corruptible power and possibke ally due to your lack of legitimacy?
The Lords of Waterdeep are pragmatic, but meddlesome. If a new power takes over Amphail, they will want to know that it will increase stability, not invite chaos. (See above for sources of chaos.) If they’re confident that things will go well, they’ll be subtle allies, or at least benevolently ignore the usurpation of the town. Chaos is something they’ll send covert agents to deal with (which may be in support of you, or may be to eliminate or control you). If chaos is great, they’ll send troops to “keep the peace” and then you’re dealing with a watch that doesn’t answer to you, negotiating with an army, or an invasion.
And that’s just fellow “good races”. You’d also have to contend with things like orcs, ogres, giants, etc. that the North tends to occasionally threaten settlements of many sizes with.
The bottom line is: how much do you like politics, and if not much, are you confident you can take the town without provoking too much opposition? How well do you know the situation on the ground? What are you local information resources and network like?
Can you work from behind the scenes to avoid being seen as the official power, and just protect Amphail as an “interested private member of the community”, pulling strings as you need without upsetting too many existing stakeholders?
How much does your DM like politics? If they do, see all the above for what you might be getting into.
If they don’t, it can go two ways:
They’ll ignore it and it’ll rarely come up, with your investment mostly showing up as background colour, if at all. No trouble, but not much real impact or recognition either.
They’ll have a bit of a crisis, not wanting to gloss over your new power base but having no idea how to handle it or whether they should even “let” you do that.
You may find it frustrating as they unreasonably block or interfere with your contribution to the fiction, or they might decide they’re out of their depth and ask a question on a site like this for how to handle it.