I think he could handle the responsibilities, but I think he would always rather be flying the ship.
Spoiler for novels.....
In the new novels Tom is the official first officer on Voyager and has settled into the role very well.
Yes, I know that (and that Chakotay would be not only pardoned but rehabilitated and promoted as the captain of Voyager with Janeway's consent) but, if I remember well, the novels are non-canon. aren't they?!
And from what I read (Taylor's novels, Mosaic & Pathways, which were a source for the series & which drew a portrait of each main characters known) and saw
the evolutuon of these same characters through 7 years, in particular the various changes that have occurred after Taylor left her position of producer (cf from s4). I tend to disagree with post-Voyager novels.
(If CBS/Paramout decided to make a post-Voyager/Nemesis series - hey, we can always dream!

- and IF some "data" about main characters (including Seven & the Doctor) were retaken from various post Voyager novels, I'd valid them, no questions asked.
However, before being accused to prevent others to dream again
, I specify that if other Voyager fans enjoy what they read in Voyager novels, it's good too!
And getting back to Tom Paris, it was quite clear, in Taylor's books, that he joined Starfleet under pressure from his father (who was already a senior officer), in order to follow the family tradition. I don't say that he never really appreciate his involvment, since it allowed him to live his piloting passion but through the series, it became became equally clear that he was just as good at entertaining creating programs. I guess that since he gave up his maverick life, one of the various priorities which changed with the arrival of B'Elena in his life and later, the one of little Miral, he aspires now to nothing less than a peaceful life. So, I would rather see him joining his three passions, in creating piloting programs for Starfleet cadets, while making him available for his family (with maybe a new arrival in the family). Alright, it would be maybe a little boring in some ways but so much safe. Same for B'Elena but in her areas of expertise (engineering). That being say, this does not prevent them to answer a call from their Voyager family, if they are needed (and to assume the role of First Officer if requested)