I was reading a piece about Soviet Historiography in the Anglophone world and the changes in the field since the onset of the Cold War, and a bit of E. H. Carr's work was brought up that I found compelling:
"Yet Carr showed how naive, almost childish, Trotskii was to remain committed to the goal of a Europe-wide revolution, especially after the collapse of the German October in 1923 and the re-consolidation of bourgeois governments between 1924 and 1926. Bukharin's commitment to the quasi-capitalist political economy of NEP would have doomed the USSR in the face of hostile encirclement and the rise of strong-state forms of fascism. Trotskii's commitment to permanent revolution would have been equally disastrous. Stalin's retreat from revolution, to the defense of socialism in one country, was no mere tactic to undermine Trotskii's influence. In Carr's telling of the story, Stalin's advocacy of a national form of Bolshevism derived from a realistic assessment of the Soviet Union in the context of world politics. Davies' empirical studies of the Soviet political economy supported Carr's view, at least about the necessity of some kind of alternative to both Bukharin's NEP and Trotskii's permanent revolution"
Putting aside Trotsky's actual conduct in Soviet politics (he didn't make many friends and was supremely arrogant by all accounts) that severely hindered any realistic chance of consolidating power even without Stalin, I think Trotsky probably would've probably been a bit more proactive and helped Soviet foreign policy in some areas but the aggressiveness proposed by him would likely lead to far worse relations with neighboring powers and the former Entente. Diplomacy with the western powers would be far worse and make any moves to contain any aggressive Fascism impossible (and empower right wing forces within Weimar to act with more of a free hand)..
I'd expect the opposite of a Red Alert scenario - Stalin's realpolitik allowed the Soviet Union some breathing room and space to recover and Trotsky's would only realize the iron ring of capitalist encirclement the Soviet propagandists envisioned. Not even to mention his style of politics being very ill suited to the realities of Soviet government was likely to alienate more than cultivate political ties that the traditional Russian political system heavily relied on.