There are two aspects that need to be considered here:
- Can you do what you propose with acceptable results?
- Should you do what you propose?
We'll look at the latter first.
Why that digital purchase is $300
Businesses like Prestige need to make more money than they spend to stay in business. Their school portrait division, Lifetouch, for example, goes to a school and photographs every student, faculty, and staff member. As part of the contract to get the school photos, they cover events, like sports, throughout the school year. They shoot club/team/group photos for the school yearbook (which is published by other companies). They do this whether anyone buys a single photo or not. They need to charge enough for the photos they sell to cover what they spend producing them, as well as make a little profit. That's the whole purpose of investing in a business and taking an economic risk.
I know a few photographers who work for the parent company that owns the Prestige brand. (Full disclosure: As a favor to some of those friends, I have done seasonal work for them in the past as a "Santa" for their holiday packages.) Sometimes they shoot schools that don't sell enough photos to cover their expenses. Sometimes they shoot schools that sell enough that they do pretty well.
For most of the past, the way such studios met their expenses and (hopefully) made money was on prints. The more prints you bought, the more they made. They even archive your images for a set period of time in which you can order more prints later if you choose. Each print, of course, has a fixed cost to produce at their national lab and ship to you, as well as a markup that is meant to help cover the expenses incurred in shooting the photo.
With a digital sale, they know full well that once they sell you a digital copy, you're not going to buy another print of that image from them. Ever. Walgreens or Costco or your home inkjet printer will be getting all of that business.
That introduces another key issue: once someone else is printing their work, they have zero control over the quality of those prints. If the prints turn out looking bad, or even "decent", instead of meeting the high quality standards they have for their own lab, it reflects poorly on them in the minds of their customers and others who may see the prints and know who took the photos.
The "digital" package is priced to discourage anyone from actually buying it unless they can make more on it than they would on the number of prints they figure someone who buys it will get printed somewhere else.
If you're going to use an image taken more or less "on spec" (for very little or no money up front in the hope that you will see the value of the product and buy it) as your profile photo on a site which can potentially lead to employment opportunities that can significantly affect your future income, shouldn't you be willing to pay the company that took that photo and presented you in the best light possible what they think it is worth? How would you feel if you were expected to work for a company that way? At the end of the day, they can pay you only what they think your work was worth?
Scanning photos for web use
Assuming you have a halfway decent scanner and use it properly, you can produce an excellent image from a high quality 8x10 photograph. The texture of the paper upon which it is printed will have some effect on just how good the scan can be. If you know how to do optimal downsizing of the resulting huge image file, you can produce a web-sized photo that will be fairly high quality. Most folks won't be able to tell the difference between a scanned 8x10 reduced to, say 400 x 500 pixels, and a 400 x 500 pixel version produced by reducing the digital file from which the print was made.
The problem with scanning a print you bought and using it in such a way is the fact that even when you buy a print, your are not buying rights to the image. Prestige still owns the copyright to that photograph. They get to decide who can use it and in what way it may be used.
Doing what you propose will almost certainly violate the terms under which you bought the 8X10" print for $35. Although they'll probably never know that you even did it, it is possible that they could find out about it and seek legal remedies. That might be as simple as sending a "cease and desist" letter requesting that you remove the photo anywhere you have posted it. Or it might be in the form of a lawsuit seeking compensatory and punitive damages for your unauthorized use of their intellectual property.
In a lawsuit, the only ones who really "win" are the lawyers for both sides. There was a recently publicized case by YouTubers Tony & Chelsea Northrup in which a company in Australia used one of his images without permission and printed it on thousands of phone cases and sold them. After a couple of years, the Northrups wound up winning the resulting lawsuit. The defendant had to pay $40K (AUS) in damages and probably another $20K (AUS) in legal fees. After Northrup paid his lawyers and the middleman he had to use to hire a lawyer in Australia that would take the case, he got between $7-8K USD!