In brief: No — in Hegel reason is not the achievement of an individual who withdraws and thinks. It is bound to recognition, to language, to institutions and to a time. The thinker who takes himself for the origin of his thoughts is in Hegel a figure of morality — and not a good one.
The argument from recognition
The analysis of lordship and bondage shows that a self-consciousness is actual only if another recognizes it as such. Whoever makes himself his own authority has none. Hegel’s formula for spirit is therefore not that of the solitary I but „the I that is We, and the We that is I“.
In the philosophy of right this has a sober form. That someone counts as a person is, according to § 209 Remark, a result of cultivation, not a property he brings with him:
It belongs to cultivation, to thinking as consciousness of the individual in the form of universality, that I be apprehended as a universal person, in which all are identical.
Groundlines, § 209 Remark
The argument from time
The Preface to the Groundlines contains the sentence that philosophy is „its own time comprehended in thoughts“, and the remark that it is as foolish to fancy that a philosophy goes beyond its present world as to think that an individual overleaps his time. The thinker thinks out of a situation he has not chosen, with a language he has not made, about relations that were there before him. That is no limitation of reason but its condition.
This is also why philosophy in Hegel always comes too late — see the owl of Minerva.
The figure he writes against
Solitary thinking has a name in the Groundlines: the conscience that lets nothing count but itself. § 137–§ 140 show how it turns into hypocrisy as soon as it becomes the sole authority: what I hold to be good is good because I hold it to be good. Hegel calls this not freedom but the „summit“ of subjectivity, which turns into its opposite.
And in § 2 Remark he wards off the related figure in the doctrine of right: the manner of „making natural or intensified feeling, one’s own breast and enthusiasm, the source of right“ — the most convenient method and „at the same time the most unphilosophical“.
What does not follow from it
Not that the individual should submit. § 132 expressly determines the „right to recognize nothing that I do not see to be rational“ as „the highest right of the subject“. It is only, Hegel adds, a formal right: the insight may be true or mere opinion, and against it stands the right of the objective. Both hold, and the relation of the two is the real subject of the second part.
Nor that truth is a matter of majorities. § 317 f. treat public opinion with a famous double verdict: it deserves to be respected as much as it deserves to be despised. Thinking in common is in Hegel not the same as the opinion of many.
The test
It can be made on one’s own reading. Whoever examines whether a transition in the Groundlines follows is doing something he must do alone — and does it on a text, with concepts and in a language he has from others. It is precisely this relation that Hegel means when he determines reason not as a faculty but as a relation.
Sources. Phenomenology of Spirit, chapter IV A. – Groundlines, Preface; § 2 Remark, § 132 and Remark, § 137–§ 140, § 187, § 209 Remark, § 315–§ 320. – Encyclopaedia (1830) §§ 424–437. – Literature. Ludwig Siep, Anerkennung als Prinzip der praktischen Philosophie, Freiburg 1979; Robert B. Brandom, A Spirit of Trust, Cambridge (Mass.) 2019; Terry Pinkard, Hegel’s Phenomenology. The Sociality of Reason, Cambridge 1994. – In the glossary: recognition, intersubjectivity, public opinion.