No.

People have made the arguments you do, but that was decades or centuries ago, and even then subject to debate. Now, that debate has quite firmly swung away from the kinds of explanations you're thinking of. These things aren't believed even by the historians arguing for the more traditional narrative. (That there was a fall, a collapse of the Roman empire, rather than a more gradual and partial transformation, something that no longer is held to be self-evident, and that this was caused by outside invasion. I.E. Peter Heather, Adrian Goldsworthy, Bryan Ward-Perkins. Scholars arguing the opposite view would include Peter Brown, Guy Halsall)

For starters: Nobody believes in any "barbarisation" anymore, where the Romans lost "martial virtues" and came to rely on "disloyal Germanic mercenaries." The Germans that served in the ranks of the later Roman army (And they were always a minority) were as loyal or trustworthy and effective as any Roman troops. The strongman-generals of Germanic descent that take such a prominent role in the narrative of the 5th century were thoroughly Romanised, both in culture and outlook.

Many of the "barbarian invasions" on a closer look have characteristics reminiscent of civil wars, especially the sack of 410. Some historians (Halsall) argue that instead of Germans conquering the empire, we should see it more as Roman subject troops (who happen to be German) taking over the region around their bases once central government collapses. (I think this explanation works better for some regions than for others, but it definitely has merit.) Hell, in other posts on this sub I've learned that people even make a case that in certain times and places the terms "Roman" and "German" no longer reflect ethnicity, but occupation.

As for how strong the later Roman army was: opinions and estimates differ wildly. Some historians argue that the late army was bigger and stronger than ever before! Others, such as Goldsworthy, who puts forth a strong argument, say that the 5th century Roman army was in fact much smaller and weaker than that of the 2nd or 4th century. But that decline had nothing to do with "settling," or with not training their troops well. Those Roman armies that existed remained formidable and won most of their battles. Rather, a large combination of factors were at work. Explanations range from outside enemies getting stronger (Heather) to a wide variety of internal factors contributing to a Roman decline. Explanations include an eroding tax-base, splintering loyalties to an increasingly ineffective central government, loss of aristocratic support, the difficulty of maintaining and paying for a large professional army in the face of all this, the ever-present strain between presenting an effective military challenge to outside raids and the risk of Roman generals gaining enough prestige to rise up in rebellion, economic troubles, inflation, population decline, climate change, and so on, and so forth, down to the occasional spate of simple bad luck and the wrong people being in charge at the wrong place in the wrong time. Oh, if you're Gibbon it's all the fault of the Christians. (Most people no longer credit this one.)

This is not the time and place to go into why the empire did fall, (Or collapse, or disintegrate, or transform, or whatever term you prefer, though I do think "transformation" is too bloodless a term for this chaotic and violent period.) even if I could do the subject justice. (Libraries could be written on the subject, and have.)

Suffice it to say that conquering Germania would have alleviated precisely none of these problems. The Romans would then have fought different enemies, perhaps. Their borders would have been even longer and more difficult to control. But honestly, it's impossible to say what exactly would have happened longe-term. There are too many changing variables at work to even begin to answer such counterfactual questions with any degree of sense. It's an intriguing scenario to consider: a Rome that stretched to the Elbe. But it can be no more than that.

Still, since none of the reasons Rome did fall had anything to do with "Not ruling over Germania" or "Not having enough territory" or anything like that, I'm confident in answering your question with a firm negative.

In the short term, it's fairly easy to say no. The Romans had two centuries of relative peace on that border, from the end of the Germanic campaigns in AD 16 to the Crisis of the Third Century.

In the long term... Really, there was no way for Rome to conquer the Germanic tribes. The distances were just too vast. Had the Romans retaken the land between the Rhine and the Weser, there were still tribes to the east, so they'd have to move on to the Elbe (and during Germanicus' reprisals, many tribes appear to have moved east of the Elbe). But beyond the Elbe was just more German tribes, and beyond that Slavic tribes and so on all the way the Pacific. No matter how far they extended their border, they would always have 'barbarian' tribes on the border.

Even just reaching the Elbe required a huge logistical effort on the part of the Romans. The German tribes had a very decentralized economy, and the villages, even if they were willing, couldn't supply the Roman forces in Germania. So supplies had to be shipped from Gaul. This meant a trip through the IJsselmeer (which was then a freshwater lake), thru Drusus' canal, and across the Wadden Sea. The North Sea storms pretty much made this passage impossible in the winter, which is why the Romans wintered along the Rhine and Lippe during their brief occupation. Reaching the Oder was right out...that required a trip around the Danish peninsula.

So, logistically, it was never really likely the Romans could have held Germania at all, and certainly not in depth, without a complete restructuring of Germanic society. Not that the Romans didn't try at places like Waldgirmes, but it was a very slow process (look how long it took to conquer the tribes in Iberia, and that was on a peninsula!).