You can't use proxies or fakes in any sanctioned event (except proxies of cards damaged during a particular tournament), so it depends on what you mean by normal tournament? So if it's not sanctioned, that depends on your store's view on proxies if they have one, in addition to what others mentioned; how your playgroup feels about you using alt art/thicker/fake cards.

It'd be for custom art
I don't know how proxy works compared with alters for example, but alters are WAY more expensive

So first directly from the MTR:

"Artistic modifications are acceptable in sanctioned tournaments, provided that the modifications do not make the card art unrecognizable, contain substantial strategic advice, or contain offensive images. Artistic modifications also may not obstruct or change the mana cost or name of the card.
The Head Judge is the final authority on acceptable cards for a tournament." http://www.wizards.com/contentresources/wizards/wpn/main/documents/magic_the_gathering_tournament_rules_pdf1.pdf

It cannot be Marked:

"Players are responsible for ensuring that their cards and/or card sleeves are not marked during the course of the tournament. A card or sleeve is considered marked if it bears something that makes it possible to identify the card without seeing its face, including scratches, discoloration, and bends.
If a player’s cards are sleeved, the cards must be examined while in the sleeves to determine if they are marked. Players should use care when sleeving their decks and should randomize their decks prior to sleeving them to reduce the possibility of cards becoming marked with a pattern. Players should also keep in mind that cards or sleeves may become worn and potentially marked through play during the course of a tournament.
The Head Judge has the authority to determine if a card in a player’s deck is marked. Judges may request that a player remove his or her current sleeves or replace any of the deck’s current sleeves immediately, or before the next round. "

So if you were to print out a card it would be considered illegal/proxy. If you were to print out a new face and glue it that would change the thickness and it would be a marked card.If you printed directly on an actual card that would likely not change the thickness but you are flirting with some illegalness as well. Now if you are not playing in a tournament/card shop and instead playing at a friends house that all that really matters is your friends opinions. If they don't care than do it, if they do then you have to either comply or convince.

that's really helpful, thank you
I'll ask my friend if they are okay with that

Fun fact, there is a corner case where proxies are now officially legal and sometimes mandatory in Legacy and Vintage!

Apparently Kess, Dissident Mage has become playable in those formats. Since she was printed in a precon, literally all versions of her are foil, which means that a great many of them are heavily warped and therefore break the thickness rule. Therefore, in order to play her in your deck, you need to go show your deck to a judge, who will provide you with proxies for the Kess's.

That only applies if your foils are curled, or if she's your only foil and too curled. Also notable, you can't get already damaged cards proxied for an event unless it's in Kess's situation (only comes in foil). I've played Kess (and alters) in large sanctioned Vintage and Legacy events with no issues, but my cards are flat though (and a lot of it is foil so they would blend in mostly the same anyway). Kess was sort of (temporarily) soft banned by CFB when judges wouldn't allow proxies at first but then they created checklist cards for them.

There was a pic of a proxy a judge made for a Kess once that was quite laughable, actually. They put a sticky note onto a card. Ugh.

But also, don't do anything suspicious like 58 nonfoils and 2 foil Jace, or 60 nonfoils but 15 foil sb cards.