Roma improving would really be a shocker, I do not expect Ranieri to make the team any better at all, I understand that it may look like a better team at the moment because of the tie, but you will see that by the end of the season they will finish badly, both at league and at Europa as well, they will not do good at all. Ranieri isn't a magician, he can't turn this team into something much better, Roma is a bad team this season and until they fix the roster issues they will stay bad.
No manager in the world, even Pep Guardiola, can't turn this roster into a winner, so betting against them is still a smart move in most games. Unless they are playing against some weaker Serie A team of course, in that case you can do whatever but even then I would just not gamble on that game instead. I can see fans being a little bit hopeful after this game, like if there is any light at all, but there is none if you ask me and they will continue to be bad this season.
AS Roma fired De Rossi too soon, the management made another mistake by appointing Ivan Juric as the next successor, which is why they are now far behind the European zone. Indeed, Claudio Ranieri has enough experience, but without preparation to build a squad that fits his strategy, it will still be difficult to achieve this season target. I think they were lucky to draw with Tottenham yesterday in the Europa League, and then they have to shift their focus to Serie A to face another tough match against Atalanta.
Claudio Ranieri has the opportunity to overhaul his line-up in the January transfer market, but that is not at all AS Roma style. The club looks very frugal in terms of transfer budget, and it seems that Claudio Ranieri has no choice but to use the available players. Artem Dovbyk who was brought in from Girona has not been able to meet expectations, and AS Roma should have been able to make Lukaku move from Chelsea permanent in the last summer transfer window.
Changing coaches is indeed a crucial step to improve team performance, but if done hastily or without careful consideration, it can actually make things worse, as is currently being experienced by AS Roma. As a result, AS Roma is now quite far behind the European zone, a situation that is certainly disappointing for a club with great ambitions. and a draw against Tottenham is a pretty good result, considering that Tottenham is currently in its best form. And you are right that the real big challenge actually comes from the domestic league, where they will face Atalanta, this will be a pretty tough test for AS Roma.
And although overhauling the line-up in the middle of the season is not their habit, and is more about utilizing existing player resources, if holding a transfer market in January can improve the team's condition, why not do it. so that at least even though this season they failed to perform well in the UEFA, they still have the opportunity to participate in the tournament next season.