No: come is only intransitive
There is an idiom to come to that means per the OED:
intransitive. To revive, recover; esp. to recover from a swoon, faint, etc.; to regain consciousness. Cf. to come to one's senses (or oneself) at Phrasal verbs 2, to come round 6 at Phrasal verbs 6.
- 2008 I blacked out. When I came to, the windscreen had come in on top of me. — Metro (Nexis) 3 June (Glasgow edition) 1
But all your examples are using to come not with a preposition but with a to-infinitive complement. The OED has this as:
I.4.c.iii. intransitive. With to-infinitive
- 2012 One night..he came to show me a chameleon he had found. — New Yorker 23 January 63/3
This is extremely common, but that doesn't make them transitive. You can tell they can't be transitive because you cannot transform them into a passive.
It’s also possible to use it with a bare infinitive.
I.4.c.i. intransitive. With bare infinitive. Chiefly in the infinitive. Cf sense I.5a. Now U.S.
- 1994 He said I ever had an idea for a show I should come see him. — R. C. Reinhart, Telling Moments 36
- 2007 I have half a mind to call the men in white coats to come take you away. — T. Myers, Hell hath No Curry xxvii. 171
The “passivization” syntactic test is a very good indicator of whether a verb is actually transitive. These are not, and come is not. It is only intransitive.
In comments the asker inquired if they OALD’s example of In time she came to love him is transitive or intransitive, and why they are saying it is transitive. Certainly it is intransitive. You can tell this by using the passive inversion syntactic test (using names of people plucked from the classic Dick and Jane):
- Jane loved Dick dearly.
- ✅ Dick was dearly loved by Jane.
You can’t do that with catenative verbs that take infinitival complements because they have no syntactic object, no substantive, to promote into subject position for a be + past participle subject–object inversion.
- In time Jane came to love Dick.
- ❌ To love Dick was Jane in time to come.
As you see, (4) is ungrammatical nonsense. Catenative verbs do not passivize, which is why they are not transitive. Here's another such example:
- Dick helped start Jane's car.
- ❌ Jane's car was helped start by Dick.
And another:
- Dick tried to start Jane's car.
- ❌ To start Jane’s car was tried by Dick.
Why does OALD call to come to INFINITIVE transitive when it is not so?
Because they’re working with a drastically reduced set of grammatical constructions and rules in order to target learners. This makes it easier to get started on the language by smoothing over technical complexities. It is a simpler model, but you should not take it too seriously because it has its drawbacks.
For the most part, if a verb is transitive, then you can passivize it in the way I have just demonstrated with no loss in meaning. This fails that test.
There are, however, transitive verbs that fail the passivization test because their inversion means something else, or doesn't mean anything at all. That's a larger subject than we need to get into here.