It has no logistics capable of supporting significant military effort at that distance, no.
Imagine you want to deploy a decent-sized modern military force - say 10,000 troops with AFVs, air support, etc. This requires huge amounts of material. Food, complex arms, spare parts, fuel. Once operations start, consumables and replacements are needed at a high rate. In WW2, a single division in action was estimated to require over 700 tons of stuff a day, and likely it requires more now due to increased complexity of weaponry.
Iran is backing up regional allies with far less. Hamas for instance is (estimated) under 20,000 strong, and doesn't really have much that's more complex than small arms - it cobbles together homemade rockets and other devices, and Iran doesn't have to supply a lot of military needs like food, medicine, etc. Years of smuggling allow these guerrilla forces enough to stockpile for one offensive, after which they will be mostly quiescent for months-years. It's really fucking hard to get stuff to them, and so once they've shot a bolt, it's a long time to the next one. It does not supply them at anything like the rate full, ongoing, conventional warfare would require.
Next, remember, Iran can only get anything to Syria by going through Turkey or Iraq, or even less favourable routes. If it wants to supply a significant Iranian military force for operations against Israel, it has to ask permission from these countries to run a supply line through their territory. It is not going to get that permission. As above, smuggling is not going to cut it.