No, you can’t use spell slots, unless you choose the class associated with your Spellcasting feature. Without loss of generality, suppose you are a Wizard who takes the Magic Initiate feat (PHB, p. 168), and pick the cleric class for the feat.
Can a Wizard take magic initiate Wizard?
Yes, a wizard can take the Magic Initiate feat and select spells from the Wizard list. The Magic Initiate feat gives you these classes to choose from: bard, cleric, druid, sorcerer, warlock, or wizard.
Does Magic initiate give Spellcasting feature?
The Magic Initiate feat gives you the ability to cast three spells—that’s spellcasting. It doesn’t give you the Spellcasting feature.
Can a magic initiate learned spell be cast with spell slots?
That’s not true. Spell slots are not per-class. If you’re a Wizard 10/Cleric 10, you can cast either class’s spells from any of your spell slots, including upcasting any of them to 6th-9th level. You just max out at 5th level spells in either class.
Is it possible for an Adventurers League to buy magical items?
For the nuance in your question about “possibly using downtime” – there are in-adventure opportunities in Adventurer’s League to buy magical items but note that there are often limitations including spending downtime. For example, in Tomb of Annihilation downtown costs and magical items sold are cited in the TOA Primer:
What’s the proper way to use magic initiate?
This is a guide to using the Magic Initiate feat correctly; in my sessions, I’ve noticed that players don’t fully realize all the crazy ways they can change their character, both in terms of roleplay and game mechanics, with it. So without further ado… Why go for Magic Initiate?
How many players can you have in Adventurers League?
All Adventurers League tables must have a minimum of three players, but not more than seven players to be considered a legal table. This number does not include the DM. Players may only play one character at a time and • they may only play their own characters.