Jesus is described in Hebrews 7:22 as εγγυος :
κατα τοσουτον κρειττονος διαθηκης γεγονεν εγγυος ιησους [Hebrews 7:22 TR]
By so much was Jesus made a surety of a better testament. [KJV]
by so much of a better covenant hath Jesus become surety, [YLT]
ἐγγὺς Strong 1451 occurs many times in the New Testament but only in this place do the KJV and YLT translate the word 'surety'. Others call it 'guarantor'. Everywhere else it is 'near' or 'nigh at hand'.
The word used in Hebrews 7:22 (εγγυος) is, however, slightly different from ἐγγὺς, and is the only time it appears in scripture. But it is simply the personification (with the masculine ending) of the concept ἐγγὺς - near or nigh at hand.
I wouldn't like to go further and try, myself, to translate εγγυος. I can only point to the underlying concept and its obvious relevance to the question at hand.
Thus the word expresses similar to Paraklete - one drawn near.
Jesus is come nigh in covenant. He is also the Messenger of the Covenant (see Mark 1:1 and Malachi 3:1.
So, a resounding 'Yes' to the question.
Jesus is also a 'comforter'.
If anything, this word εγγυος is an expression of an even closer union than Paraklete. It is the very expression of nearness. It is nearness personified.
Wherefore in all things it behoved him to be made like unto his brethren [Hebrews 2:17, KJV]
Then another is 'called beside' as well.
EDIT Note : Some give this text the meaning of 'Covenant Head'.