Possibly, but that is not what it actually says.
Reasonably any spacecraft can mount any component that fits inside it. Saying that a 1 Dt component can be fitted to a 2001 Dt ship, but not to a 2000 Dt ship is a little too magical for me.
If we force this way of interpreting the rules, you could probably fit A rated jump, maneuver and PP drives in a 25 dton ship, along with its fuel for a jump, so not allowing ships under 100 dtons to jump is equally magical....
I understand that Capital Ship rules are only for Capital Ships.
They mainly include batteries bearing according configuration, a percentage based drives system, Core computers, spinals, sections and little else that really difers from basic ships.
Of course, there is a gray área on the higher end of basic rues or lower end of Capital Ships ones, where both systems could overlap, but I don't believe they should be merged.
I once designed a 800 dton semi-military ship, J3 M3. WIth the same capacities, it costed about MCr 750 and had 200 dtons cargo built with core rules, and about MCr 420 and 250 dtons cargo with HG rules. Symilar effects occured in CT.
That's why I don't think merging systems to be a good idea...
Core computers have no stated size, but given that any core computer, even the biggest, easily fit into the 10 Dt bridge/command module of a 2001 Dt "capital" ship it can't be all that large.
So I don't find it impossible that smaller spacecraft can mount core computers, especially 5 TLs later.
On the Core Compuers specifically:
As explained in MgT:HG page 65, the Core Computers central computers that control the drives and the
multiple distributed computer networks any Capital Ship has.
Of course, this does not apply to ACS, and even less to small crafts.
It's also specified that their tonnage is included among the command modules one, Those control modules have a tonnage, for the minimal Capital Ship (3000 dtons) of 30 dtons (one 15 dtons module per section, 2 sections), and grow as the ship goes bigger.
Of course, not all of it is occupied by the Core computer, and unfortunatelly the rules don't talk about it any more, but I guess they should occupy several of them, and don't fit in most ACS, and less so in a small craft.
You're right in that the letter of the rules don't forbide it, but here's where I say the logics should apply. As a lawyer would say, the "spirit of the law".