Can accusativus cum inf. depend on ευ εχει, ορθώς έχει and similar expressions. Smythe does not mention this, however in 1984, he alludes to inf. dependent on quasi impersonal verbs.
Specifically for ἔχει? The LSJ occurs to me as the place to research this. And we have:
B.II.2. freq. with Advbs. of manner, εὖ ἔχει Od.24.245,
etc.; καλῶς ἔχει, κακῶς ἔχει, it is, is going on
well or ill, v. καλός, κακός (but fut. σχήσειν καλῶς
will turn out well, D.1.9, cf. 18.45; εὖ σχήσει
S.Aj.684); οὕτως . . σχεῖν to turn out, happen thus,
Pl.Ap.39b; οὕτως ἔχει so the case stands, Ar.Pl.110;
οὕτως ἐχόντων, Lat. cum res ita se habeant,
X.An.3.2.10; ὡς ὧδ’ ἐχόντων S.Aj.981; οὕτω χρὴ διὰ
στέρνων ἔχειν Id.Ant.639; οὕτως ἔ. περί τινος
X.Mem.4.8.7, cf. Hdt.6.16; πρός τι D.9.45; τῇδ’ ἔ.
S.Ph.1336; κοσμίως ἔ. Ar.Th.854; ἥδιον ἔ. πρός τινας
D.9.63; ὡς εἶχε just as he was, Hdt.1.114; ὥσπερ
εἶχε Th.1.134, X.HG4.1.30; ὡς ἔχω how I am,
Ar.Lys.610; ὥσπερ ἔχομεν Th.3.30; τἀναντία εἶχεν
D.9.41; ἀσφαλέως, ἀναγκαίως ἔχει, = ἀσφαλές,
ἀναγκαῖόν ἐστι, Hdt.1.86,9.27; καλῶς ἔχει no, I
thank you, v. καλός.
A.III.1. c.inf., have means or power to do, to be able, c.
aor. inf., Il.7.217, 16.110, etc.: c. pres. inf.,
Od.18.364, etc.; πόλλ’ ἂν λέγειν ἔχοιμι S.Ph.1047:
sts. with inf. omitted or supplied from context,
ἀλλ’ οὔ πως ἔτι εἶχε he could not, Il.17.354; οἷά κ’
ἔχωμεν so far as we be able, Od.15.281; ἐξ οἵων ἔχω
S.El.1379; ὅσον εἶχες E.IA1452; ὡς ἔχω Id.Hec.614.
They don’t seem to mix, from what I can tell by the entry. But maybe there is an example of it happening?
Did a quick search through some of the Perseus documents, found this lovely gem in Plutarch:
ὅθεν εὖ ἔχει τὸ τὴν νύκτα καὶ τὸν ὕπνον ἐν μέσῳ θεμένους καὶ ποιήσαντας ἱκανὸν διάλειμμα καὶ διάστημα καθαροὺς αὖθις ὥσπερ ἐξ ὑπαρχῆς καὶ ‘νέα ἐφʼ ἡμέρῃ φρονέοντας’ κατὰ Δημόκριτον ἀνίστασθαι. ’ Plut. QC 3.6.4
Plutarch. (1892). Moralia. (G. N. Bernardakis, Ed.) (Vol. 4, p. 125). Medford, MA: Teubner.
ὅθεν εὖ ἔχει τὸ τὴν νύκτα καὶ τὸν ὕπνον ἐν μέσῳ θεμένους καὶ ποιήσαντας ἱκανὸν διάλειμμα καὶ διάστημα καθαροὺς αὖθις ὥσπερ ἐξ ὑπαρχῆς καὶ ‘νέα ἐφʼ ἡμέρῃ φρονέοντας’ κατὰ Δημόκριτον ἀνίστασθαι. ’ Plut. QC 3.6.4
Maybe I’m misreading, but isn’t that just εὖ ἔχει with τὸ…ἀνίστασθαι as the subject, rather than an infinitive dependent on the verb?
Also, while I think that I understand what’s going on in the sentence, I’d hate to try putting it into English.
Ah, good observation, probably, the τό would seem to indicate that. And this is a fairly typical Plutarchean sentence… 
Therefore, according to Democritus, it is good for those who place their night and sleep in between, making due intervals and pauses, to wake up refreshed again as from the beginning thinking about new things during the day.