Chichornio, it seems very strange that your only option is to use sRGB. I’m not familiar with the Epson scan software, so maybe that’s the case, but I can hardly believe so. Isn’t there some color management tab where you can select the profile to use? It may be worthwhile to play around with your software to see if you can find another option.
If you don’t insert a profile when scanning, then typically you’d have a scanner profile that you’d assign to your scans when you open them in PS. A scanner profile may be included in your scanner software. Usually it would be installed when you install the software. So, when you open a scan in PS, see if you can find your scanner profile and assign that profile to your scan, then convert to aRGB. Another alternative is to create your own scanner profile, but I won’t go into that possibility now.
(Maybe a little explanation of how your scanner works will help. I apologize if I’m rehashing information you already know. Your model of scanner captures color in a way that is likely unique to your scanner, not a standard sRGB or aRGB color space. Hence, the usual procedure to assign your scanner profile first rather than a straight assignment of a standard color profile. If you select a standard color profile in your scanner software, your software effectually does such a two step process. In other words, say you have a computer program that translates documents. If you have a document written in French and want it translated to English, you’d first tell the program that the original document is in French (in other words you’d assign French to that document), then convert that document into English. Instead, if you took the French document and just told the translation program that your document was in English (in other words you assigned English), you’d end up with gibberish. Well, assigning the wrong color profile to a scan is similar, but the results are not as dramatic as in my translation analogy.
Regarding your last question, the short answer is no. I hope you can bear with another analogy. Think of your scanner color as water. Your scanner can output a number of different colors to fill up a gallon jug. sRGB, however, only holds a quart. So, to get your scanner colors to fit into a quart container, your scanner software has to throw away a bunch of colors. Once those colors are gone, you can’t get them back. Actually, the colors that don't fit into the gamut of sRGB, for example, are changed into colors that do fit. So, you end up with a smaller number of colors.